Daniel Voigt Godoy - Deep Learning with PyTorch Step-by-Step A Beginner’s Guide-leanpub

In code, the implementation of the alpha version of EWMA looks like this:
def EWMA(past_value, current_value, alpha):
return (1- alpha) * past_value + alpha * current_value
For computing it over a series of values, given a period, we can define a function
like this:
def calc_ewma(values, period):
alpha = 2 / (period + 1)
result = []
for v in values:
try:
prev_value = result[-1]
except IndexError:
prev_value = 0
new_value = EWMA(prev_value, v, alpha)
result.append(new_value)
return np.array(result)
In the try..except block, you can see that, if there is no previous value for the
EWMA (as in the very first step), it assumes a previous value of zero.
The way the EWMA is constructed has its issues—since it does not need to keep
track of all the values inside its period, in its first steps, the "average" will be way
off (or biased). For an alpha=0.1 (corresponding to the 19-periods average), the
very first "average" will be exactly the first value divided by ten.
To address this issue, we can compute the bias-corrected EWMA:
Equation 6.8 - Bias-corrected EWMA
The beta in the formula above is the same as before: 1 - alpha. In code, we can
implement the correction factor like this:
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