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. 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)