a$)$ The table below shows data supplied from the New York Stock Exchange $($NYSE$)$ on the average price

of Trane Technologies $($TT$)$ stock over a nine$-$week period:

Determine the forecasted values using exponential smoothing method with smoothing constants $=0\mathrm{.}5$

and $=0\mathrm{.}83.$ Which smoothing constant appears to provide the more accurate forecasts based on MSE?

Explain.

$(6$ marks$)$

b$)$ Consider the quarterly sales data observed in the last four years for Heavvy Equipment Co$.$ in the table

below:

i$.$ Compute seasonal indexes and adjusted seasonal indexes for the quarterly data.

$(8$ marks$)$

ii$.$ Deseasonalise the time series.

$(3$ marks$)$

iii. Explain how one would go about determining the seasonally adjusted forecast for the four quarters

of the fifth year using the deseasonalised data from part $($ii$).$