$4\mathrm{.}2$ Reconsider the time series data shown in Table E$4\mathrm{.}1.$

a$.$ Use simple exponential smoothing with the optimum value of $$ to smooth the first $40$ time periods of this data $($you can find the optimum value from Minitab$).$ How well does this smoothing procedure work? Compare the results with those obtained in

Exercise $4\mathrm{.}1.$

b$.$ Makeone$-$step$-$aheadforecastsofthelast$10$observations.Deter$-$ mine the forecast errors. Compare these forecast errors with those from Exercise $4\mathrm{.}1.$ How much has using the optimum value of the smoothing constant improved the forecasts?