Question

Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.

Week	Sales (1,000s of gallons)
1	17
2	21
3	19
4	23
5	18
6	16
7	18
8	16
9	20
10	18
11	13
12	20

(a) Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.)

Week	Time Series Value	Weighted Moving Average Forecast
1	17
2	21
3	19
4	23	?
5	18	?
6	16	?
7	18	?
8	16	?
9	20	?
10	18	?
11	13	?
12	20	?

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

MSE =

Answer 1

a)

Week	Value	Weighted moving Average		Error	Error²
1	17	-	-	-	-
2	21	-	-	-	-
3	19	-	-	-	-
4	23	17*1/6 + 21*1/3 + 19*1/2 =	19.33	3.67	13.44
5	18	21*1/6 + 19*1/3 + 23*1/2 =	21.33	-3.33	11.11
6	16	19*1/6 + 23*1/3 + 18*1/2 =	19.83	-3.83	14.69
7	18	23*1/6 + 18*1/3 + 16*1/2 =	17.83	0.17	0.03
8	16	18*1/6 + 16*1/3 + 18*1/2 =	17.33	-1.33	1.78
9	20	16*1/6 + 18*1/3 + 16*1/2 =	16.67	3.33	11.11
10	18	18*1/6 + 16*1/3 + 20*1/2 =	18.33	-0.33	0.11
11	13	16*1/6 + 20*1/3 + 18*1/2 =	18.33	-5.33	28.44
12	20	20*1/6 + 18*1/3 + 13*1/2 =	15.83	4.17	17.36
Total				-2.83	98.08

b)

MSE = ∑(A-F)²/n = 98.083/9 = 10.9