According to the Wikipedia page on moving averages, "This is also why sometimes an EMA is referred to as an $N$-day EMA. Despite the name suggesting there are $N$ periods, the terminology only specifies the $\alpha$ factor. $N$ is not a stopping point for the calculation in the way it is in an SMA or WMA."
I was very shocked to read this. It seems to be suggesting that the sequence of weights used to compute the Exponential Moving Average via discrete convolution with historical price data goes on forever. I understand that the sum of an infinite number of weights can converge to $1$, but not how an infinite weight function sequence could be convolved with a finite sequence of historical market price data.
How is an $N$-period Exponential Moving Average computed as the convolution of a weight function and historical data? Is the weight function sequence indeed infinite, or does it only contain $N (\pm 1?)$ elements, or does it contain as many elements as historical data points are available $(\pm 1?)$ which is usually greater than $N$? This distinction seems important because adding additional elements will re-normalize the significant elements given that all elements sum to $1$. What is a typical example of how this convolution product would be formulated?
