Consider the following time series data:

Month Value

1 24

2 13

3 20

4 12

5 19

6 23

7 15

a. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 8.

b. Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 8.

c. Compare the three-week moving average forecast with the exponential smoothing forecast using a = 0.2. Which appears to provide the better forecast based on MSE?

d. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for a = 0.2.

\begin{tabular}{|c|c|} \hline 93 & 90 \\ \hline 102 & 90 \\ \hline 84 & 90 \\ \hline 110 & 91 \\ \hline 93 & 91 \\ \hline 105 & 91 \\ \hline 109 & 91 \\ \hline 91 & 92 \\ \hline 104 & 92 \\ \hline 95 & 92 \\ \hline 98 & 92 \\ \hline 91 & 93 \\ \hline 104 & 93 \\ \hline 104 & 94 \\ \hline 106 & 95 \\ \hline 95 & 95 \\ \hline 106 & 95 \\ \hline 92 & 95 \\ \hline 101 & 96 \\ \hline 95 & 96 \\ \hline 109 & 96 \\ \hline 95 & 96 \\ \hline 101 & 96 \\ \hline 105 & 91 \\ \hline 104 & 91 \\ \hline 104 & 100 \\ \hline 105 & 100 \\ \hline 110 & 91 \\ \hline 101 & 91 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline 93 & 90 \\ \hline 102 & 90 \\ \hline 84 & 90 \\ \hline 110 & 91 \\ \hline 93 & 91 \\ \hline 105 & 91 \\ \hline 109 & 91 \\ \hline 91 & 92 \\ \hline 104 & 92 \\ \hline 95 & 92 \\ \hline 98 & 92 \\ \hline 91 & 93 \\ \hline 104 & 93 \\ \hline 104 & 94 \\ \hline 106 & 95 \\ \hline 95 & 95 \\ \hline 106 & 95 \\ \hline 92 & 95 \\ \hline 101 & 96 \\ \hline 95 & 96 \\ \hline 109 & 96 \\ \hline 95 & 96 \\ \hline 101 & 96 \\ \hline 105 & 91 \\ \hline 104 & 91 \\ \hline 104 & 100 \\ \hline 105 & 100 \\ \hline 110 & 91 \\ \hline 101 & 91 \\ \hline \end{tabular}