#StackBounty: #time-series #moving-average #filter #moving-window How does choosing an even window size actually add a cyclical compone…

Bounty: 50

I am new to Time Series Analysis. Say, we have a time series $(y_{t})_{t}$ that we want to filter with a moving average filter. I have been told that we should choose the window size $L$ of the filter to be uneven. Apparently, if it were even, this would introduce another cyclical component into the data. My question is: why? Why would an even window size introduce a cyclical component, while an uneven window size would not?

There seems to be no mathematical justification for this…

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