NumPy version of “Exponential weighted moving average”, equivalent to pandas.ewm().mean()

Question

How do I get the exponential weighted moving average in NumPy just like the following in pandas?

import pandas as pd
import pandas_datareader as pdr
from dat         


        

Answer 1

Here's my implementation for 1D input arrays with infinite window size. As it uses large numbers, it works only with input arrays with elements of absolute value < 1e16, when using float32, but that should normally be the case.

The idea is to reshape the input array into slices of a limited length, so that no overflow occurs, and then doing the ewm calculation with each slice separately.

def ewm(x, alpha):
    """
    Returns the exponentially weighted mean y of a numpy array x with scaling factor alpha
    y[0] = x[0]
    y[j] = (1. - alpha) * y[j-1] + alpha * x[j],  for j > 0

    x -- 1D numpy array
    alpha -- float
    """

    n = int(-100. / np.log(1.-alpha)) # Makes sure that the first and last elements in f are very big and very small (about 1e22 and 1e-22)
    f = np.exp(np.arange(1-n, n, 2) * (0.5 * np.log(1. - alpha))) # Scaling factor for each slice
    tmp = (np.resize(x, ((len(x) + n - 1) // n, n)) / f * alpha).cumsum(axis=1) * f # Get ewm for each slice of length n

    # Add the last value of each previous slice to the next slice with corresponding scaling factor f and return result
    return np.resize(tmp + np.tensordot(np.append(x[0], np.roll(tmp.T[n-1], 1)[1:]), f * ((1. - alpha) / f[0]), axes=0), len(x))