The Following Data Shows the Quarterly Profit (In Thousands of Dollars)

Essay

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years. $$\begin{array} { | c | c | c | } \hline \text { Year } & \text { Quarter } & \text { Profit (\$1000s) } \\\hline 1 & 1 & 45 \\\hline 1 & 2 & 51 \\\hline 1 & 3 & 72 \\\hline 1 & 4 & 50 \\\hline 2 & 1 & 49 \\\hline 2 & 2 & 45 \\\hline 2 & 3 & 79 \\\hline 2 & 4 & 54 \\\hline 3 & 1 & 42 \\\hline 3 & 2 & 58 \\\hline 3 & 3 & 70 \\\hline 3 & 4 & 56 \\\hline\end{array}$$
a. Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter.
b. Compare the three-period moving average forecast with the exponential smoothing forecast using α = 0.3. Which appears to provide the better forecast based on MSE?