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}