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 is an implementation using NumPy that is equivalent to using df.ewm(alpha=alpha).mean(). After reading the documentation, it is just a few matrix operations. The trick is constructing the right matrices.

It is worth noting that because we are creating float matrices, you can quickly eat through your memory if the input array is too large.

import pandas as pd
import numpy as np

def ewma(x, alpha):
    '''
    Returns the exponentially weighted moving average of x.

    Parameters:
    -----------
    x : array-like
    alpha : float {0 <= alpha <= 1}

    Returns:
    --------
    ewma: numpy array
          the exponentially weighted moving average
    '''
    # Coerce x to an array
    x = np.array(x)
    n = x.size

    # Create an initial weight matrix of (1-alpha), and a matrix of powers
    # to raise the weights by
    w0 = np.ones(shape=(n,n)) * (1-alpha)
    p = np.vstack([np.arange(i,i-n,-1) for i in range(n)])

    # Create the weight matrix
    w = np.tril(w0**p,0)

    # Calculate the ewma
    return np.dot(w, x[::np.newaxis]) / w.sum(axis=1)

Let's test its:

alpha = 0.55
x = np.random.randint(0,30,15)
df = pd.DataFrame(x, columns=['A'])
df.ewm(alpha=alpha).mean()

# returns:
#             A
# 0   13.000000
# 1   22.655172
# 2   20.443268
# 3   12.159796
# 4   14.871955
# 5   15.497575
# 6   20.743511
# 7   20.884818
# 8   24.250715
# 9   18.610901
# 10  17.174686
# 11  16.528564
# 12  17.337879
# 13   7.801912
# 14  12.310889

ewma(x=x, alpha=alpha)

# returns:
# array([ 13.        ,  22.65517241,  20.44326778,  12.1597964 ,
#        14.87195534,  15.4975749 ,  20.74351117,  20.88481763,
#        24.25071484,  18.61090129,  17.17468551,  16.52856393,
#        17.33787888,   7.80191235,  12.31088889])