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
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