QUESTION $315$Pts $-$ Time Series & Forecasting Part A

The prices of a backpack over the past $12$ months are shown in Question $3$ Template. Use the table to answer the following questions $(15$pt$).$

a$)$ Use a $3-$month moving average to smooth the time series and forecast the price for Month $13(3$pt$)$

b$)$ Use a $3-$month weighted moving average to smooth the time series. Use a weight of $\mathrm{.}4$ for the most recent period, $\mathrm{.}3$ for the next period back, and $\mathrm{.}3$ for the third period back. Forecast the price for Month $13(3$pt$)$

c$)$ For each of the method, include a time series plot including actual and forecast vales, title your chart, add axis labels and edit the legend $(3$Pts$)$

d$)$ Compute MSE for the two smoothing methods in $($a$)$ and $($b$)$ above $(4$pt$)$

e$)$ Which of the two methods do you prefer and why? $(2$pt$)$