$1)$ Use a three period moving average model to forecast the demand in January of $1993.$ Also calculate the RMSE for this model. Use the table below:

Month Demand $($A$)$ Demand $($F$)($A$-$F$)2$

Jan$-9225\mathrm{.}6$

Feb$-9224\mathrm{.}7$

Mar$-9221\mathrm{.}3$

April$-9213\mathrm{.}9$

May$-9212\mathrm{.}6$

June$-9218$

July$-9221\mathrm{.}5$

Aug$-9222\mathrm{.}3$

Sep$-9230\mathrm{.}7$

Oct$-9215$

Nov$-9213\mathrm{.}8$

Dec $22\mathrm{.}6$

$2)$ Use a five period moving average model to forecast the demand in January of $1993.$ Also calculate the RMSE for this model. Use the table below to carry out your calculations. How does this model compare with the three period model?

Month Demand $($A$)$ Demand $($F$)($A$-$F$)2$

Jan$-9225\mathrm{.}6$

Feb$-9224\mathrm{.}7$

Mar$-9221\mathrm{.}3$

April$-9213\mathrm{.}9$

May$-9212\mathrm{.}6$

June$-9218$

July$-9221\mathrm{.}5$

Aug$-9222\mathrm{.}3$

Sep$-9230\mathrm{.}7$

Oct$-9215$

Nov$-9213\mathrm{.}8$

Dec $22\mathrm{.}6$

$3)$ Given the below demand data what are the exponential smoothing forecasts for periods Feb$-$December using a$=0\mathrm{.}10.$ Assume F$1=$D$1.$ Also calculate RMSE for this model

Month Demand $($A$)$ Demand $($F$)($A$-$F$)2$

Jan$-9225\mathrm{.}6$

Feb$-9224\mathrm{.}7$

Mar$-9221\mathrm{.}3$

April$-9213\mathrm{.}9$

May$-9212\mathrm{.}6$

June$-9218$

July$-9221\mathrm{.}5$

Aug$-9222\mathrm{.}3$

Sep$-9230\mathrm{.}7$

Oct$-9215$

Nov$-9213\mathrm{.}8$

Dec$-9222\mathrm{.}6$