a$.$ Write down the forecast $($F$13)$ for Week $13$ using a $3-$week weighted moving average, with weights $5,3,1($with $5$ being applied to the most recent value, then $3,$ then $1).(2$pts$)$

b$.$ Write down the forecast $($F$13)$ for Week $13$ using exponential smoothing with alpha $=\mathrm{.}45.$ Please start the forecast at Week $1,$ with Week $1$ actual number sold $=22($A$1=22)$ and the forecast for Week $1=22($F$1=22),$ then continue through Week $13$ to find F$13.(2$pts$)$

c$.$ Create forecasts for all possible time periods $($not just Week $13)$ using the above methods $($weighted moving average $$ Weeks $4-12,$ exponential smoothing $$ Weeks $1-12).$

Then calculate errors $($E$)$ for each forecast method for the time periods $4-12($Week $4,5,6,...,12).$ Then use these error terms to calculate the MAD, MSE, and MAPE for each forecast method.

Fill out the table below with the results $($i$.$e$.,$ MAD, MSA, and MAPE values for each forecasting method$).(6$pts$)$

$3-$week weighted moving average with weights: $5,3,1($with $5$ being applied to the most recent value, then $3,$ then $1)$ Exponential smoothing with alpha $=\mathrm{.}45$

MAD

MSE

MAPE

d$.$

Which method do you think is best and why?