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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