Refer again to the gasoline sales time series data in the following table. Using

Question

Refer again to the gasoline sales time series data in the following table.

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. Use rounded for two decimal places values for intermediate colculations.

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. Round your answer to two decimal places.

MSE =  ____

Prefer the Weighted/Unweighted moving average here.

Week Sales (1000s of gallons) 1 19 2 21 3 21 4 23 5 20 6 18 7 22 8 17 9 23 10 23 11 13 12 23

Explanation / Answer

MSE = [(Dt-Ft)²]/n = 164.92 / 9 = 18.32

Since this is greater than 10.22, we prefer the unweighted moving average than the weighted moving average.

Week Sales (Dt) Weighted Moving
Average Forecast (Ft) Forecast
Error
(Dt - Ft) (Error)2 1 19 2 21 3 21 4 23 20.67 2.33 5.43 5 20 22.00 -2.00 4.00 6 18 21.17 -3.17 10.05 7 22 19.50 2.50 6.25 8 17 20.33 -3.33 11.09 9 23 18.83 4.17 17.39 10 23 20.83 2.17 4.71 11 13 22.00 -9.00 81.00 12 23 18.00 5.00 25.00 Total 164.92

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