$*$SOLVE IN EXCEL$*$ A Simple forecasting method for weekly sales of DVD drives used by a local computer dealer is to form the average of the two most recent sales Figures. Suppose sales for the drives for the past $6$ weeks were

$\backslash$table$[[$Week$,1,2,3,4,5,6],[$Sales$,86,75,72,83,132,65]]$

a$.$ Determine the one$-$step$-$ahead forecasts made for period $4$ through $6$ using $MA(3)$ and WMA$(3).$

b$.$ Compute $($i$)$ MAD, $($ii$)$ MSE, and $($iii$)$ MAPE of MA$(3)$ and WMA$(3).$ Explain which method gives better result.

$2.$ Handy, Inc., produces a solar$-$powered electronic calculator that has experienced the following monthly sales history for the first four months of the year, in thousands of units:

$\backslash$table$[[$January$,$February,March,April$],[23\mathrm{.}3,72\mathrm{.}3,30\mathrm{.}3,15\mathrm{.}5]]$

If the forecast for January was $25,$ determine the one$-$step$-$ahead forecasts for February through May using exponential smoothing with a smoothing constant of $=0\mathrm{.}15.$

$3.$ Consider the $6-$month time series data on demand given in the following table. Use the Holt's method to predict demand for months of $3-6$ at month $2($i$.$e$.,F_{2,3},F_{2,4},F_{2,5}$ and $($:$F_{2,6}\}.$ Assume $==0\mathrm{.}3.G_1=24$

$\backslash$table$[[$Month$,1,2,3,4,5,6],[$Demand$,220,250,280,295,315,340]]$