Consider the following gasoline sales time series data. Click onthe datafile logo to reference the data.
Week | Sales (1000s of gallons) |
1 Â Â Â | 16Â Â Â |
2 Â Â Â | 21Â Â Â |
3 Â Â Â | 19Â Â Â |
4 Â Â Â | 24Â Â Â |
5 Â Â Â | 18Â Â Â |
6 Â Â Â | 16Â Â Â |
7 Â Â Â | 19Â Â Â |
8 Â Â Â | 17Â Â Â |
9 Â Â Â | 23Â Â Â |
10 Â Â Â | 20Â Â Â |
11 Â Â Â | 15Â Â Â |
12 Â Â Â | 22Â Â Â |
a. Using a weight of 1/2 for the most recentobservation, 1/3 for the second most recent observation, and 1/6third the most recent observation, compute a three-week weightedmoving average for the time series (to 2 decimals). Enter negativevalues 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 movingaverage in part (a).
MSE =
Do you prefer this weighted moving average to the unweightedmoving average? Remember that the MSE for the unweighted movingaverage is 13.69.
Prefer the unweighted moving average here; it has a(greater/smaller) MSE.
c. Suppose you are allowed to choose anyweights as long as they sum to 1. Could you always find a set ofweights that would make the MSE at least as small for a weightedmoving average than for an unweighted moving average?
(Yes/No)
