Consider the following gasoline sales time series data. Click on the datafile logo to reference the data. Week Sales (1000s of gallons) 1 16 2 20 3 20 4 23 5 18 6 17 8 19 9 23 10 19 11 14 12 21 a....


Consider the following gasoline sales time series data. Click on the datafile logo to reference the data.



























































Week

Sales (1000s of gallons)
116
220
320
423
518
617
819
923
1019
1114
1221



a. Using a weight of  1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 the most recent observation, compute a three-week weighted moving average for the time series (to 2 decimals). Enter negative values as negative numbers.






































































































































Week



Time-Series Value

Weighted Moving
Average Forecast


Forecast
Error




(Error)2

1
2
3
4
5
6
7
8
9
10
11
12
Total



b. Compute the MSE for the weighted moving average in part (a).
MSE =


Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 8.90.
Prefer the unweighted moving average here; it has a (greater/smaller) MSE.



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 at least as small for a weighted moving average than for an unweighted moving average? (Yes/ No)



Jun 06, 2022
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