N&O: Chapter $2,$ #$19.(15$ points$)$

Parts $($a$)$ through $($c$)$ are based on the following observations of the demand for a certain part

stocked at a parts supply depot during the calendar year.

Month Demand Month Demand

January $89$ July $223$

February $57$ August $286$

March $144$ September $212$

April $221$ October $275$

May $177$ November $188$

June $280$ December $312$

$($a$)$ Using a four$-$month moving average, determine the one$-$step$-$ahead forecasts for July through

December.

$($b$)$ Using a four$-$month moving average, determine the two$-$step$-$ahead forecast for July through

December. $($Hint: The two$-$step$-$ahead forecast for July is based on the observed demands in

February through May.$)$

$($c$)$ Compute the MAD for the forecasts obtained in problems $($a$)$ and $($b$).$ Which method gave

better results? Based on forecasting theory, which method should have given better results?