Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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?
Transcribed Image Text:Problem 15-08
Refer again to the gasoline sales time series data in Table 15.1.
GASOLINE SALES TIME SERIES
Week
Sales (1000s of gallons)
17
2
3
21
19
23
18
4
5
6.
16
7
20
8
18
22
10
20
15
22
11
12
Transcribed Image Text: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. Use
rounded for two decimal places values for intermediate colculations.
Weighted Moving
Forecast
(Error)2
Week
Sales
Average Forecast
Error
1
17
2
21
3
19
4
23
5
18
6
16
7
20
8
18
9
22
10
20
11
15
12
22
Total
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. Round your answer to two decimal places.
MSE =
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