In many applications, a time series decomposition (i.e., time series filtering) is used to separate or decompose a time series xt into its trend, seasonal, and irregular components. In some of these applications, the decomposition relationship is assumed to be additive: Xt =TREND t +SEASONAL t +Irregular t
While in other applications the decomposition relationship is assumed to be multiplicative: Xt =TREND t *SEASONAL t * Irregular t
1:Explain the merits of such decomposition methods, and mention a particular example of a time series where you believe that implementing a decomposition technique is justified. Explain your reason(s) for selecting such an example.
2:Explain in what situations you would prefer to use an additive decomposition method, and in what situations you would prefer to use a multiplicative method in your time series decomposition.
Each question about 250 words
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