Please solve Q7,8,9. Highlight your final answers. Write a 300-word discussion of the forecasting method.

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Chapter 6 Time Series Analysis and Forecasting 7. Refer to the gasoline sales time series data in Table 6.1. a. Compute four-week and five-week moving averages for the time series. b. Compute the MSE for the four-week and five-week moving average forecasts. c. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 10.22. 8. Refer again to the gasoline sales time series data in Table 6.1. a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. b. Compute the MSE for the weighted moving average in part (a). Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 10.22. c. Suppose you are allowed to choose any weights as long as they sum to 1. Could you always find a set of weights that would make the MSE smaller for a weighted moving average than for an unweighted moving average? Why or why not? 9. With the gasoline time series data from Table 6.1, show the exponential smoothing fore- casts using a = 0.1. a. Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of a 0.1 or a = 0.2 for the gasoline sales time series? b. Are the results the same if you apply MAE as the measure of accuracy? C. What are the results if MAPE is used?