Problems on Moving Averages Problems $16$ through $21$ are based on the following data. Observations of the demand for a certain part stocked at a parts supply depot during the calendar year $2013$ were onthemandonthemand January $89$ July $223$ February $57$ August $286$ March $144$ September $212$ April $221$ October $275$ May $177$ November $188$ June $280$ December $31216.$ Determine the one$-$step$-$ahead forecasts for the demand for January $2014$ using $3-,6-,$ and $12-$month moving averages. $17.$ Using a four$-$month moving average, determine the one$-$step$-$ahead forecasts for July through December $2013.18.$ Using a four$-$month moving average, determine the two$-$step$-$ahead forecast for July through December $2013.($Hint: The two$-$step$-$ahead forecast for July is based on the observed demands in February through May.$)19.$ Compute the MAD for the forecasts obtained in Problems $17$ and $18.$ Which method gave better results? Based on forecasting theory, which method should have given better results? $20.$ Compute the one$-$step$-$ahead three$-$month and six$-$month moving$-$average forecasts for July through December. What effect does increasing N from $3$ to $6$ have on the forecasts? $21.$ What would an MA$(1)$ forecasting method mean? Compare the accuracy of MA$(1)$ and MA$(4)$ forecasts for July through December $2013.$