Refer again to the gasoline sales time series data in the following table. Using
ID: 2796625 • Letter: R
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 moving average here.
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?
Week Sales (1000s of gallons) 1 17 2 22 3 20 4 24 5 18 6 14 7 22 8 16 9 22 10 22 11 13 12 21Explanation / Answer
The forecast for week 4 = ( 0.5 x 20 + 0.33 x 22 + 0.166 x 17)
The forecast for week 4 = 20.08
week 5 = ( 0.5 x 24 + 0.33 x 20 + 0.166 x 22)
week 5 = 22.25
week 6 = ( 0.5 x 18 + 0.33 x 24 + 0.166 x 20)
week 6 = 20.24
week 7 = ( 0.5 x 14 + 0.33 x 18 + 0.166 x 24)
week 7 = 16.92
week 8 = ( 0.5 x 22 + 0.33 x 14 + 0.166 x 18)
week 8 = 18.60
week 9 = ( 0.5 x 16+ 0.33 x 22 + 0.166 x 14)
week 9 = 17.58
week 10 = ( 0.5 x 22+ 0.33 x 16 + 0.166 x 22)
week 10 = 19.93
week 11 = ( 0.5 x 22+ 0.33 x 22 + 0.166 x 16)
week 11= 20.91
week 12 = ( 0.5 x 13 + 0.33 x 22 + 0.166 x 22)
week 12 = 17.41
error = actual sales - forecasted sales
error2 = (actual sales - forecasted sales)2
MSE = Total error2 / number of weeks
MSE = 204.24975 / 12
MSE = 17.02
The moving average is preferred than the weighted moving average because MSE is high for weighted moving average.
The most recent past is a better predictor of the future than the distant past , hence larger weights should be given to the most recent observations. However it is not possible to find a set of weights that would make the MSE smaller for a weighted moving average than for an unweighted moving average.
Week Sales Weighted Moving Forecast (Error)2 Average Forecast Error 1 17 2 22 3 20 4 24 6.694 17.306 299.49764 5 18 7.417333333 10.5826667 111.99283 6 14 6.746666667 7.25333333 52.610844 7 22 5.641333333 16.3586667 267.60598 8 16 6.202666667 9.79733333 95.98774 9 22 5.861333333 16.1386667 260.45656 10 22 6.644 15.356 235.80674 11 13 6.972 6.028 36.336784 12 21 5.804 15.196 230.91842 Total 1591.2135Related Questions
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