Classical decomposition

Here, it is described how to decompose a time series. I'm wondering about step 1.

We are going to compute the trend-cycle component. If the seasonal period m is odd, we should use m-MA. If m is even, we should use 2 * m-MA. This doesn't make sense to me.

The previous subsection describes how to compute m-MA.
A moving average of order m can be written as
Screenshot from 2020-04-06 13-35-19
where m = 2k + 1. This implies that k = (m-1)/2. If m is odd, then k is an integer. However, if m is even, k is not an integer and the formula does not makes sense to me. Doubling m will still give an even m and a non-integer k. In my opinion it would have made more sense to use a (m+1)-MA if m was even.

Referred here by Forecasting: Principles and Practice, by Rob J Hyndman and George Athanasopoulos


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