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

Let’s take the first alternative and expand the equation a bit:
Equation 6.4 - EWMA - expanded edition
The first element is taken at face value, but all the remaining elements are
discounted based on their corresponding lags.
"What is a lag?"
It is simply the distance, in units of time, from the current value. So, the value of
feature x one time unit in the past is the value of feature x at lag one.
After working out the expression above, we end up with an expression where each
term has an exponent depending on the corresponding number of lags. We can use
this information to make a sum out of it:
Equation 6.5 - EWMA - lag-based
In the expression above, T is the total number of observed values. So, an EWMA
takes every value into account, no matter how far in the past it is. But, due to the
weight (the discount factor), the older a value gets, the less it contributes to the
sum.
Higher values of alpha correspond to rapidly shrinking weights;
that is, older values barely make a difference.
Let’s see how the weights are distributed over the lags for two averages, an EWMA
with alpha equals one-third and a simple five-period moving average.
456 | Chapter 6: Rock, Paper, Scissors