Question

Refer again to the gasoline sales time series data in the following table.

Week	Sales (1000s of gallons)
1	18
2	22
3	20
4	26
5	18
6	17
7	21
8	19
9	23
10	23
11	16
12	24

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 calculations. Use minus sign for negative values.

Week	Sales	Weighted Moving Average Forecast	Forecast Error	(Error)2
1	18
2	22
3	20
4	26
5	18
6	17
7	21
8	19
9	23
10	23
11	16
12	24
			Total

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.

Answer 1

Week	Sales	Weighted Moving	Forecast	(Error)2
		Average Forecast	Error
1	18
2	22
3	20
4	26	20.33	5.67	32.11
5	18	23.33	-5.33	28.44
6	17	21.00	-4.00	16.00
7	21	18.83	2.17	4.69
8	19	19.17	-0.17	0.03
9	23	19.33	3.67	13.44
10	23	21.33	1.67	2.78
11	16	22.33	-6.33	40.11
12	24	19.50	4.50	20.25
			Total	157.86
			MSE=average=	17.54

from above MSE =17.54

as MSE is less for  unweighted moving average ; therefore one must prefer  unweighted moving average