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.
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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Transcribed Image Text: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.
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