$4\mathrm{.}2$

Year $1234567891011$

Demand $795913812139117$

a$)$ Plot the above data on a graph. Do you observe any trend, cycles,

or random variations?

b$)$ Starting in year $4$ and going to year $12,$ forecast demand using a

three$-$year moving average. Plot your forecast on the same graph

as the original data.

c$)$ Starting in year $4$ and going to year $12,$ forecast demand using a

three$-$year moving average with weights of $0\mathrm{.}1,0\mathrm{.}3,$ and $0\mathrm{.}6,$ using

$0\mathrm{.}6$ for the most recent year. Plot this forecast on the same graph.

d$)$ As you compare forecasts with the original data, which seems to

give the better results? PX $4\mathrm{.}3$ Refer to Problem $4\mathrm{.}2.$ Develop a forecast for years $2$

through $12$ using exponential smoothing with a $50\mathrm{.}4$ and a forecast for year $1$ of $6.$ Plot your new forecast on a graph with the

actual data and the naive forecast. Based on a visual inspection,

which forecast is better? PX $4\mathrm{.}4$ A cheque$-$processing centre uses exponential smoothing to forecast the number of incoming cheques each month. The

number of cheques received in June was $40$ million, while the forecast was $42$ million. A smoothing constant of $0\mathrm{.}2$ is used.

a$)$ What is the forecast for July?

b