Problem 21 Is there a linear filter W that satisfies the following two properties? (1) W leaves linear trends invariant.

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Problem 21 Is There A Linear Filter W That Satisfies The Following Two Properties 1 W Leaves Linear Trends Invariant 1 (171.62 KiB) Viewed 47 times

Problem 21 Is there a linear filter W that satisfies the following two properties? (1) W leaves linear trends invariant. (2) All seasonalities of period length 4 (and only those) are eliminated. If yes, specify W. If no, justify why such a moving average does not exist. Note: A moving average that eliminates seasonalities of length 4 will, of course, also eliminate seasonalities of length 2. However, this property is not important here and does not need to be considered. It is only necessary to ensure that the moving average does not, for example, also eliminate seasonalities of length 3, 5, 8 or others. >