The sales of the last $12$ months in a computer company occur immediately. Respond by giving procedures and answers.

MONTH $/$ SALES $($millions of $$)$

January $20$

February $24$

March $29$

April $32$

May $37$

June $47$

July $53$

August $62$

September $64$

October $36$

November $23$

December $29$

a$)$ Use a three$-$month moving average to forecast sales for January of the following year.

b$)$ Use a four$-$month moving average to forecast next year's January sales.

c$)$ Compare the performance of the two methods using the mean absolute deviation as the performance criterion. What method would you recommend?

d$)$ Compare the performance of the two methods using the mean percentage error as the performance criterion. What method would you recommend?

Consider the data above:

a$)$ Use a weighted moving average to forecast next year's January sales. Use the weights $(3/6),(2/6)$ and $(1/6),$ giving more weight to the most recent data.

b$)$ Use exponential smoothing with $=0\mathrm{.}6,0\mathrm{.}4,0\mathrm{.}2$ to forecast the February sale of the next year. Suppose the initial forecast for January was $$22$ million.