Question $4$:

The data in the table below give quarterly sales of a product at the a department store.

a$)$ Find the moving averages forecasting with order $4$ for the sales data. Report your results in the following table.

b$)$ Find the centered moving average with order for for the sales data. Report your results in the following table.

c$)$ The centered moving average trend $($CMAT$)$ is estimated as CMAT $=23\mathrm{.}5+0\mathrm{.}8($time$).$ Report your results in the following table.

d$)$ K$-$mart made a forecast of oligopoly sales at the beginning of time $1.$ The

forecasted sale is $20.$ If a smoothing constant of $0\mathrm{.}3$ is used, what is the

exponentially smoothed forecast for time $4,$ the fourth quarter of year $1?$

e$)$ Can you find any pattern$($s$)$ in the time series by observation? What is the

suitable forecasting method to address this pattern$($s$)?$