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Part 1

Suppose you have been given a time series and are asked to forecast the values of the time series during one or more of the future periods. Explain a few of the actions that you will undertake as your preliminary investigation of the given time series before you decide which particular forecasting method you should use.

Part 2

In many applications, a time series decomposition (i.e., time series filtering) is used to separate or decompose a time series into its trend, seasonal, and irregular components. In some of these applications, the decomposition relationship is assumed to be additive, while in other applications the decomposition relationship is assumed to be multiplicative. Describe the situations when you would prefer to use an additive decomposition method, and situations when you would use a multiplicative method in your time series decomposition. Furthermore, discuss a specific example of a real-life time series of interest to some enterprise, and for which you would prescribe a multiplicative decomposition.

Note: an additive decomposition of time series Xt is a decomposition of type:

Xt=trendt+seasonalt+irregulart ,

and a multiplicative decomposition is of type:

Xt=trendt×seasonalt×irregulart