| 
                    1
                 | 
                                    
                                                     | 
                
                 | 
                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    2
                 | 
                                    
                                                     | 
                
                 | 
                Technical Analysis Factors  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    3
                 | 
                                    
                                                     | 
                
                 | 
                --------------------------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    4
                 | 
                                    
                                                     | 
                
                 | 
                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    5
                 | 
                                    
                                                     | 
                
                 | 
                from bottleneck import (  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    6
                 | 
                                    
                                                     | 
                
                 | 
                    nanargmax,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    7
                 | 
                                    
                                                     | 
                
                 | 
                    nanmax,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    8
                 | 
                                    
                                                     | 
                
                 | 
                    nanmean,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    9
                 | 
                                    
                                                     | 
                
                 | 
                    nansum,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    10
                 | 
                                    
                                                     | 
                
                 | 
                )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    11
                 | 
                                    
                                                     | 
                
                 | 
                from numbers import Number  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    12
                 | 
                                    
                                                     | 
                
                 | 
                from numpy import (  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    13
                 | 
                                    
                                                     | 
                
                 | 
                    abs,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    14
                 | 
                                    
                                                     | 
                
                 | 
                    arange,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    15
                 | 
                                    
                                                     | 
                
                 | 
                    average,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    16
                 | 
                                    
                                                     | 
                
                 | 
                    clip,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    17
                 | 
                                    
                                                     | 
                
                 | 
                    diff,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    18
                 | 
                                    
                                                     | 
                
                 | 
                    exp,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    19
                 | 
                                    
                                                     | 
                
                 | 
                    fmax,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    20
                 | 
                                    
                                                     | 
                
                 | 
                    full,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    21
                 | 
                                    
                                                     | 
                
                 | 
                    inf,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    22
                 | 
                                    
                                                     | 
                
                 | 
                    isnan,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    23
                 | 
                                    
                                                     | 
                
                 | 
                    log,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    24
                 | 
                                    
                                                     | 
                
                 | 
                    NINF,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    25
                 | 
                                    
                                                     | 
                
                 | 
                    sqrt,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    26
                 | 
                                    
                                                     | 
                
                 | 
                    sum as np_sum,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    27
                 | 
                                    
                                                     | 
                
                 | 
                )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    28
                 | 
                                    
                                                     | 
                
                 | 
                from numexpr import evaluate  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    29
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    30
                 | 
                                    
                                                     | 
                
                 | 
                from zipline.pipeline.data import USEquityPricing  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    31
                 | 
                                    
                                                     | 
                
                 | 
                from zipline.pipeline.mixins import SingleInputMixin  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    32
                 | 
                                    
                                                     | 
                
                 | 
                from zipline.utils.control_flow import ignore_nanwarnings  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    33
                 | 
                                    
                                                     | 
                
                 | 
                from zipline.utils.input_validation import expect_types  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    34
                 | 
                                    
                                                     | 
                
                 | 
                from .factor import CustomFactor  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    35
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    36
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    37
                 | 
                                    
                                                     | 
                
                 | 
                class Returns(CustomFactor):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    38
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    39
                 | 
                                    
                                                     | 
                
                 | 
                    Calculates the percent change in close price over the given window_length.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    40
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    41
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs**: [USEquityPricing.close]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    42
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    43
                 | 
                                    
                                                     | 
                
                 | 
                    inputs = [USEquityPricing.close]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    44
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    45
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, close):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    46
                 | 
                                    
                                                     | 
                
                 | 
                        out[:] = (close[-1] - close[0]) / close[0]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    47
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    48
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    49
                 | 
                                    
                                                     | 
                
                 | 
                class RSI(CustomFactor, SingleInputMixin):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    50
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    51
                 | 
                                    
                                                     | 
                
                 | 
                    Relative Strength Index  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    52
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    53
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs**: [USEquityPricing.close]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    54
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    55
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length**: 15  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    56
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    57
                 | 
                                    
                                                     | 
                
                 | 
                    window_length = 15  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    58
                 | 
                                    
                                                     | 
                
                 | 
                    inputs = (USEquityPricing.close,)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    59
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    60
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, closes):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    61
                 | 
                                    
                                                     | 
                
                 | 
                        diffs = diff(closes, axis=0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    62
                 | 
                                    
                                                     | 
                
                 | 
                        ups = nanmean(clip(diffs, 0, inf), axis=0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    63
                 | 
                                    
                                                     | 
                
                 | 
                        downs = abs(nanmean(clip(diffs, -inf, 0), axis=0))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    64
                 | 
                                    
                                                     | 
                
                 | 
                        return evaluate(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    65
                 | 
                                    
                                                     | 
                
                 | 
                            "100 - (100 / (1 + (ups / downs)))",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    66
                 | 
                                    
                                                     | 
                
                 | 
                            local_dict={'ups': ups, 'downs': downs}, | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    67
                 | 
                                    
                                                     | 
                
                 | 
                            global_dict={}, | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    68
                 | 
                                    
                                                     | 
                
                 | 
                            out=out,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    69
                 | 
                                    
                                                     | 
                
                 | 
                        )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    70
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    71
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    72
                 | 
                                    
                                                     | 
                
                 | 
                class SimpleMovingAverage(CustomFactor, SingleInputMixin):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    73
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    74
                 | 
                                    
                                                     | 
                
                 | 
                    Average Value of an arbitrary column  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    75
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    76
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs**: None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    77
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    78
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length**: None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    79
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    80
                 | 
                                    
                                                     | 
                
                 | 
                    # numpy's nan functions throw warnings when passed an array containing only  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    81
                 | 
                                    
                                                     | 
                
                 | 
                    # nans, but they still returns the desired value (nan), so we ignore the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    82
                 | 
                                    
                                                     | 
                
                 | 
                    # warning.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    83
                 | 
                                    
                                                     | 
                
                 | 
                    ctx = ignore_nanwarnings()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    84
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    85
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, data):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    86
                 | 
                                    
                                                     | 
                
                 | 
                        out[:] = nanmean(data, axis=0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    87
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    88
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    89
                 | 
                                    
                                                     | 
                
                 | 
                class WeightedAverageValue(CustomFactor):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    90
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    91
                 | 
                                    
                                                     | 
                
                 | 
                    Helper for VWAP-like computations.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    92
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    93
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    94
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    95
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    96
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    97
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, base, weight):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    98
                 | 
                                    
                                                     | 
                
                 | 
                        out[:] = nansum(base * weight, axis=0) / nansum(weight, axis=0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    99
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    100
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    101
                 | 
                                    
                                                     | 
                
                 | 
                class VWAP(WeightedAverageValue):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    102
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    103
                 | 
                                    
                                                     | 
                
                 | 
                    Volume Weighted Average Price  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    104
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    105
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs:** [USEquityPricing.close, USEquityPricing.volume]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    106
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    107
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    108
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    109
                 | 
                                    
                                                     | 
                
                 | 
                    inputs = (USEquityPricing.close, USEquityPricing.volume)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    110
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    111
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    112
                 | 
                                    
                                                     | 
                
                 | 
                class MaxDrawdown(CustomFactor, SingleInputMixin):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    113
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    114
                 | 
                                    
                                                     | 
                
                 | 
                    Max Drawdown  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    115
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    116
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    117
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    118
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    119
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    120
                 | 
                                    
                                                     | 
                
                 | 
                    ctx = ignore_nanwarnings()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    121
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    122
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, data):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    123
                 | 
                                    
                                                     | 
                
                 | 
                        drawdowns = fmax.accumulate(data, axis=0) - data  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    124
                 | 
                                    
                                                     | 
                
                 | 
                        drawdowns[isnan(drawdowns)] = NINF  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    125
                 | 
                                    
                                                     | 
                
                 | 
                        drawdown_ends = nanargmax(drawdowns, axis=0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    126
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    127
                 | 
                                    
                                                     | 
                
                 | 
                        # TODO: Accelerate this loop in Cython or Numba.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    128
                 | 
                                    
                                                     | 
                
                 | 
                        for i, end in enumerate(drawdown_ends):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    129
                 | 
                                    
                                                     | 
                
                 | 
                            peak = nanmax(data[:end + 1, i])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    130
                 | 
                                    
                                                     | 
                
                 | 
                            out[i] = (peak - data[end, i]) / data[end, i]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    131
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    132
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    133
                 | 
                                    
                                                     | 
                
                 | 
                class AverageDollarVolume(CustomFactor):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    134
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    135
                 | 
                                    
                                                     | 
                
                 | 
                    Average Daily Dollar Volume  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    136
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    137
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs:** [USEquityPricing.close, USEquityPricing.volume]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    138
                 | 
                                    
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    139
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    140
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                    inputs = [USEquityPricing.close, USEquityPricing.volume]  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
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                | 
                    143
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, close, volume):  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                        out[:] = nanmean(close * volume, axis=0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    145
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                class _ExponentialWeightedFactor(SingleInputMixin, CustomFactor):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                    Base class for factors implementing exponential-weighted operations.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    152
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                    inputs : length-1 list or tuple of BoundColumn  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                        The expression over which to compute the average.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                    window_length : int > 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                        Length of the lookback window over which to compute the average.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                    decay_rate : float, 0 < decay_rate <= 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                        Weighting factor by which to discount past observations.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                        When calculating historical averages, rows are multiplied by the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                        sequence::  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                            decay_rate, decay_rate ** 2, decay_rate ** 3, ...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                    Methods  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                    weights  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                    from_span  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                    from_halflife  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                    from_center_of_mass  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                    params = ('decay_rate',) | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    177
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    178
                 | 
                                    
                                                     | 
                
                 | 
                    @staticmethod  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                    def weights(length, decay_rate):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    180
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    181
                 | 
                                    
                                                     | 
                
                 | 
                        Return weighting vector for an exponential moving statistic on `length`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    182
                 | 
                                    
                                                     | 
                
                 | 
                        rows with a decay rate of `decay_rate`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    183
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    184
                 | 
                                    
                                                     | 
                
                 | 
                        return full(length, decay_rate) ** arange(length + 1, 1, -1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    185
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    186
                 | 
                                    
                                                     | 
                
                 | 
                    @classmethod  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    187
                 | 
                                    
                                                     | 
                
                 | 
                    @expect_types(span=Number)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    188
                 | 
                                    
                                                     | 
                
                 | 
                    def from_span(cls, inputs, window_length, span):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    189
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    190
                 | 
                                    
                                                     | 
                
                 | 
                        Convenience constructor for passing `decay_rate` in terms of `span`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    191
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    192
                 | 
                                    
                                                     | 
                
                 | 
                        Forwards `decay_rate` as `1 - (2.0 / (1 + span))`.  This provides the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    193
                 | 
                                    
                                                     | 
                
                 | 
                        behavior equivalent to passing `span` to pandas.ewma.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    194
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    195
                 | 
                                    
                                                     | 
                
                 | 
                        Example  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    196
                 | 
                                    
                                                     | 
                
                 | 
                        -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    197
                 | 
                                    
                                                     | 
                
                 | 
                        .. code-block:: python  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    198
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    199
                 | 
                                    
                                                     | 
                
                 | 
                            # Equivalent to:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    200
                 | 
                                    
                                                     | 
                
                 | 
                            # my_ewma = EWMA(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    201
                 | 
                                    
                                                     | 
                
                 | 
                            #    inputs=[USEquityPricing.close],  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    202
                 | 
                                    
                                                     | 
                
                 | 
                            #    window_length=30,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    203
                 | 
                                    
                                                     | 
                
                 | 
                            #    decay_rate=(1 - (2.0 / (1 + 15.0))),  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    204
                 | 
                                    
                                                     | 
                
                 | 
                            # )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    205
                 | 
                                    
                                                     | 
                
                 | 
                            my_ewma = EWMA.from_span(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    206
                 | 
                                    
                                                     | 
                
                 | 
                                inputs=[USEquityPricing.close],  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    207
                 | 
                                    
                                                     | 
                
                 | 
                                window_length=30,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    208
                 | 
                                    
                                                     | 
                
                 | 
                                span=15,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    209
                 | 
                                    
                                                     | 
                
                 | 
                            )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    210
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    211
                 | 
                                    
                                                     | 
                
                 | 
                        Note  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    212
                 | 
                                    
                                                     | 
                
                 | 
                        ----  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    213
                 | 
                                    
                                                     | 
                
                 | 
                        This classmethod is provided by both  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    214
                 | 
                                    
                                                     | 
                
                 | 
                        :class:`ExponentialWeightedMovingAverage` and  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    215
                 | 
                                    
                                                     | 
                
                 | 
                        :class:`ExponentialWeightedMovingStdDev`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    216
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    217
                 | 
                                    
                                                     | 
                
                 | 
                        if span <= 1:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    218
                 | 
                                    
                                                     | 
                
                 | 
                            raise ValueError(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    219
                 | 
                                    
                                                     | 
                
                 | 
                                "`span` must be a positive number. %s was passed." % span  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    220
                 | 
                                    
                                                     | 
                
                 | 
                            )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    221
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    222
                 | 
                                    
                                                     | 
                
                 | 
                        decay_rate = (1.0 - (2.0 / (1.0 + span)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    223
                 | 
                                    
                                                     | 
                
                 | 
                        assert 0.0 < decay_rate <= 1.0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    224
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    225
                 | 
                                    
                                                     | 
                
                 | 
                        return cls(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    226
                 | 
                                    
                                                     | 
                
                 | 
                            inputs=inputs,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    227
                 | 
                                    
                                                     | 
                
                 | 
                            window_length=window_length,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    228
                 | 
                                    
                                                     | 
                
                 | 
                            decay_rate=decay_rate,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    229
                 | 
                                    
                                                     | 
                
                 | 
                        )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    230
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    231
                 | 
                                    
                                                     | 
                
                 | 
                    @classmethod  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    232
                 | 
                                    
                                                     | 
                
                 | 
                    @expect_types(halflife=Number)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    233
                 | 
                                    
                                                     | 
                
                 | 
                    def from_halflife(cls, inputs, window_length, halflife):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    234
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    235
                 | 
                                    
                                                     | 
                
                 | 
                        Convenience constructor for passing ``decay_rate`` in terms of half  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    236
                 | 
                                    
                                                     | 
                
                 | 
                        life.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    237
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    238
                 | 
                                    
                                                     | 
                
                 | 
                        Forwards ``decay_rate`` as ``exp(log(.5) / halflife)``.  This provides  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    239
                 | 
                                    
                                                     | 
                
                 | 
                        the behavior equivalent to passing `halflife` to pandas.ewma.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    240
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    241
                 | 
                                    
                                                     | 
                
                 | 
                        Example  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    242
                 | 
                                    
                                                     | 
                
                 | 
                        -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    243
                 | 
                                    
                                                     | 
                
                 | 
                        .. code-block:: python  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    244
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    245
                 | 
                                    
                                                     | 
                
                 | 
                            # Equivalent to:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    246
                 | 
                                    
                                                     | 
                
                 | 
                            # my_ewma = EWMA(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    247
                 | 
                                    
                                                     | 
                
                 | 
                            #    inputs=[USEquityPricing.close],  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    248
                 | 
                                    
                                                     | 
                
                 | 
                            #    window_length=30,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    249
                 | 
                                    
                                                     | 
                
                 | 
                            #    decay_rate=np.exp(np.log(0.5) / 15),  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    250
                 | 
                                    
                                                     | 
                
                 | 
                            # )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    251
                 | 
                                    
                                                     | 
                
                 | 
                            my_ewma = EWMA.from_halflife(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    252
                 | 
                                    
                                                     | 
                
                 | 
                                inputs=[USEquityPricing.close],  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    253
                 | 
                                    
                                                     | 
                
                 | 
                                window_length=30,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    254
                 | 
                                    
                                                     | 
                
                 | 
                                halflife=15,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    255
                 | 
                                    
                                                     | 
                
                 | 
                            )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    256
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    257
                 | 
                                    
                                                     | 
                
                 | 
                        Note  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    258
                 | 
                                    
                                                     | 
                
                 | 
                        ----  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    259
                 | 
                                    
                                                     | 
                
                 | 
                        This classmethod is provided by both  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    260
                 | 
                                    
                                                     | 
                
                 | 
                        :class:`ExponentialWeightedMovingAverage` and  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    261
                 | 
                                    
                                                     | 
                
                 | 
                        :class:`ExponentialWeightedMovingStdDev`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    262
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    263
                 | 
                                    
                                                     | 
                
                 | 
                        if halflife <= 0:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    264
                 | 
                                    
                                                     | 
                
                 | 
                            raise ValueError(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    265
                 | 
                                    
                                                     | 
                
                 | 
                                "`span` must be a positive number. %s was passed." % halflife  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    266
                 | 
                                    
                                                     | 
                
                 | 
                            )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    267
                 | 
                                    
                                                     | 
                
                 | 
                        decay_rate = exp(log(.5) / halflife)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    268
                 | 
                                    
                                                     | 
                
                 | 
                        assert 0.0 < decay_rate <= 1.0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    269
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    270
                 | 
                                    
                                                     | 
                
                 | 
                        return cls(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    271
                 | 
                                    
                                                     | 
                
                 | 
                            inputs=inputs,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    272
                 | 
                                    
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                            window_length=window_length,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    273
                 | 
                                    
                                                     | 
                
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                            decay_rate=decay_rate,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    274
                 | 
                                    
                                                     | 
                
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                        )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    275
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    276
                 | 
                                    
                                                     | 
                
                 | 
                    @classmethod  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    277
                 | 
                                    
                                                     | 
                
                 | 
                    def from_center_of_mass(cls, inputs, window_length, center_of_mass):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    278
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    279
                 | 
                                    
                                                     | 
                
                 | 
                        Convenience constructor for passing `decay_rate` in terms of center of  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    280
                 | 
                                    
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                        mass.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    281
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    282
                 | 
                                    
                                                     | 
                
                 | 
                        Forwards `decay_rate` as `1 - (1 / 1 + center_of_mass)`.  This provides  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    283
                 | 
                                    
                                                     | 
                
                 | 
                        behavior equivalent to passing `center_of_mass` to pandas.ewma.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    284
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    285
                 | 
                                    
                                                     | 
                
                 | 
                        Example  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    286
                 | 
                                    
                                                     | 
                
                 | 
                        -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    287
                 | 
                                    
                                                     | 
                
                 | 
                        .. code-block:: python  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    288
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    289
                 | 
                                    
                                                     | 
                
                 | 
                            # Equivalent to:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    290
                 | 
                                    
                                                     | 
                
                 | 
                            # my_ewma = EWMA(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    291
                 | 
                                    
                                                     | 
                
                 | 
                            #    inputs=[USEquityPricing.close],  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    292
                 | 
                                    
                                                     | 
                
                 | 
                            #    window_length=30,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    293
                 | 
                                    
                                                     | 
                
                 | 
                            #    decay_rate=(1 - (1 / 15.0)),  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    294
                 | 
                                    
                                                     | 
                
                 | 
                            # )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    295
                 | 
                                    
                                                     | 
                
                 | 
                            my_ewma = EWMA.from_center_of_mass(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    296
                 | 
                                    
                                                     | 
                
                 | 
                                inputs=[USEquityPricing.close],  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    297
                 | 
                                    
                                                     | 
                
                 | 
                                window_length=30,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    298
                 | 
                                    
                                                     | 
                
                 | 
                                center_of_mass=15,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    299
                 | 
                                    
                                                     | 
                
                 | 
                            )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    300
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    301
                 | 
                                    
                                                     | 
                
                 | 
                        Note  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    302
                 | 
                                    
                                                     | 
                
                 | 
                        ----  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    303
                 | 
                                    
                                                     | 
                
                 | 
                        This classmethod is provided by both  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    304
                 | 
                                    
                                                     | 
                
                 | 
                        :class:`ExponentialWeightedMovingAverage` and  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    305
                 | 
                                    
                                                     | 
                
                 | 
                        :class:`ExponentialWeightedMovingStdDev`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    306
                 | 
                                    
                                                     | 
                
                 | 
                        """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    307
                 | 
                                    
                                                     | 
                
                 | 
                        return cls(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    308
                 | 
                                    
                                                     | 
                
                 | 
                            inputs=inputs,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    309
                 | 
                                    
                                                     | 
                
                 | 
                            window_length=window_length,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    310
                 | 
                                    
                                                     | 
                
                 | 
                            decay_rate=(1.0 - (1.0 / (1.0 + center_of_mass))),  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    311
                 | 
                                    
                                                     | 
                
                 | 
                        )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    312
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    313
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    314
                 | 
                                    
                                                     | 
                
                 | 
                class ExponentialWeightedMovingAverage(_ExponentialWeightedFactor):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    315
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    316
                 | 
                                    
                                                     | 
                
                 | 
                    Exponentially Weighted Moving Average  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    317
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    318
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    319
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    320
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    321
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    322
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    323
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    324
                 | 
                                    
                                                     | 
                
                 | 
                    inputs : length-1 list/tuple of BoundColumn  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    325
                 | 
                                    
                                                     | 
                
                 | 
                        The expression over which to compute the average.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    326
                 | 
                                    
                                                     | 
                
                 | 
                    window_length : int > 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    327
                 | 
                                    
                                                     | 
                
                 | 
                        Length of the lookback window over which to compute the average.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    328
                 | 
                                    
                                                     | 
                
                 | 
                    decay_rate : float, 0 < decay_rate <= 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    329
                 | 
                                    
                                                     | 
                
                 | 
                        Weighting factor by which to discount past observations.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    330
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    331
                 | 
                                    
                                                     | 
                
                 | 
                        When calculating historical averages, rows are multiplied by the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    332
                 | 
                                    
                                                     | 
                
                 | 
                        sequence::  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    333
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    334
                 | 
                                    
                                                     | 
                
                 | 
                            decay_rate, decay_rate ** 2, decay_rate ** 3, ...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    335
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    336
                 | 
                                    
                                                     | 
                
                 | 
                    Notes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    337
                 | 
                                    
                                                     | 
                
                 | 
                    -----  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    338
                 | 
                                    
                                                     | 
                
                 | 
                    - This class can also be imported under the name ``EWMA``.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    339
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    340
                 | 
                                    
                                                     | 
                
                 | 
                    See Also  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    341
                 | 
                                    
                                                     | 
                
                 | 
                    --------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    342
                 | 
                                    
                                                     | 
                
                 | 
                    :func:`pandas.ewma`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    343
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    344
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, data, decay_rate):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    345
                 | 
                                    
                                                     | 
                
                 | 
                        out[:] = average(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    346
                 | 
                                    
                                                     | 
                
                 | 
                            data,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    347
                 | 
                                    
                                                     | 
                
                 | 
                            axis=0,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    348
                 | 
                                    
                                                     | 
                
                 | 
                            weights=self.weights(len(data), decay_rate),  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    349
                 | 
                                    
                                                     | 
                
                 | 
                        )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    350
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    351
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    352
                 | 
                                    
                                                     | 
                
                 | 
                class ExponentialWeightedMovingStdDev(_ExponentialWeightedFactor):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    353
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    354
                 | 
                                    
                                                     | 
                
                 | 
                    Exponentially Weighted Moving Standard Deviation  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    355
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    356
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Inputs:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    357
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    358
                 | 
                                    
                                                     | 
                
                 | 
                    **Default Window Length:** None  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    359
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    360
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    361
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    362
                 | 
                                    
                                                     | 
                
                 | 
                    inputs : length-1 list/tuple of BoundColumn  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    363
                 | 
                                    
                                                     | 
                
                 | 
                        The expression over which to compute the average.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    364
                 | 
                                    
                                                     | 
                
                 | 
                    window_length : int > 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    365
                 | 
                                    
                                                     | 
                
                 | 
                        Length of the lookback window over which to compute the average.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    366
                 | 
                                    
                                                     | 
                
                 | 
                    decay_rate : float, 0 < decay_rate <= 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    367
                 | 
                                    
                                                     | 
                
                 | 
                        Weighting factor by which to discount past observations.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    368
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    369
                 | 
                                    
                                                     | 
                
                 | 
                        When calculating historical averages, rows are multiplied by the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    370
                 | 
                                    
                                                     | 
                
                 | 
                        sequence::  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    371
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    372
                 | 
                                    
                                                     | 
                
                 | 
                            decay_rate, decay_rate ** 2, decay_rate ** 3, ...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    373
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    374
                 | 
                                    
                                                     | 
                
                 | 
                    Notes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    375
                 | 
                                    
                                                     | 
                
                 | 
                    -----  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    376
                 | 
                                    
                                                     | 
                
                 | 
                    - This class can also be imported under the name ``EWMSTD``.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    377
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    378
                 | 
                                    
                                                     | 
                
                 | 
                    See Also  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    379
                 | 
                                    
                                                     | 
                
                 | 
                    --------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    380
                 | 
                                    
                                                     | 
                
                 | 
                    :func:`pandas.ewmstd`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    381
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    382
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    383
                 | 
                                    
                                                     | 
                
                 | 
                    def compute(self, today, assets, out, data, decay_rate):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    384
                 | 
                                    
                                                     | 
                
                 | 
                        weights = self.weights(len(data), decay_rate)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    385
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    386
                 | 
                                    
                                                     | 
                
                 | 
                        mean = average(data, axis=0, weights=weights)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    387
                 | 
                                    
                                                     | 
                
                 | 
                        variance = average((data - mean) ** 2, axis=0, weights=weights)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    388
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    389
                 | 
                                    
                                                     | 
                
                 | 
                        squared_weight_sum = (np_sum(weights) ** 2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    390
                 | 
                                    
                                                     | 
                
                 | 
                        bias_correction = (  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    391
                 | 
                                    
                                                     | 
                
                 | 
                            squared_weight_sum / (squared_weight_sum - np_sum(weights ** 2))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    392
                 | 
                                    
                                                     | 
                
                 | 
                        )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    393
                 | 
                                    
                                                     | 
                
                 | 
                        out[:] = sqrt(variance * bias_correction)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    394
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    395
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    396
                 | 
                                    
                                                     | 
                
                 | 
                # Convenience aliases.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    397
                 | 
                                    
                                                     | 
                
                 | 
                EWMA = ExponentialWeightedMovingAverage  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    398
                 | 
                                    
                                                     | 
                
                 | 
                EWMSTD = ExponentialWeightedMovingStdDev  | 
            
            
                                                        
            
                                    
            
            
                | 
                    399
                 | 
                                    
                                                     | 
                
                 | 
                 |