Question $1$: For a product, PSF$-008,$ the following table provides the data of demand observed during $1996.$

a$)$ Determine the one$-$month$-$ahead demand forecasts for eligible

$20$p$)$ months through two$-$month, four$-$month and six$-$month moving averages methods

b$)$ Compute mean$-$squared error $($MSE$)$ for each moving averages method based on the results obtained in part a and compare

Op$)$ these three methods to interpret which one is better suited to forecast demand

C$)$ Forecast demand for March $1997$ from July $1996$ and for May $1997$ from November $1996$ through four$-$month moving averages and estimate the demand distributions for March

$30$p$)1997$ and May $1997.($Be careful that if you are forecasting from July $1996,$ then you have not observed true demand in August to December $1996$ yet!$)$

d$)$ In addition to the one$-$step$-$ahead forecasts made through two$-$month moving averages method in part a$,$ make two$-$stepahead and three$-$step$-$ahead forecasts for the eligible months

$20$p$)$ in $1996.$ Based on the results, which of one$-$step$-$a he ad forecasting, two$-$step$-$ahead forecasting and three$-$step$-$ahead forecasting is more unbiased? Why?

e$)$ Assume that we are currently in July $1996$ and have already observed demand from January $1996$ through June $1996.$ By taking the

op$)$ me$-$step$-$ahead forecast made through faur$-$month moving a verages method as the initial forecast for July $1996,$ forecast the de mand from August $1996$ through January $1997$ through exponential smouthing with $\backslash (\backslash$alpha$=0\mathrm{.}3\backslash ).$

Show the each calculations