5. Forecasting Weekly Data. Consider the following time series data:

a. Construct a time series plot. What type of pattern exists in the data?

b. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7.

c. Use a 5 0.2 to compute the exponential smoothing values for the time series.

Compute MSE and a forecast for week 7.

d. Compare the three-week moving average forecast with the exponential smoothing forecast using a 5 0.2. Which appears to provide the better forecast based on MSE? Explain.

e. 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 5 0.2.