Question

Consider the following gasoline sales time series data.

Week	Sales (1000s of gallons)
1	18
2	22
3	20
4	24
5	17
6	15
7	19
8	17
9	23
10	19
11	14
12	23

a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 third 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 17.43.
Prefer the unweighted moving average here; it has a - Select your answer -(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?
- Select your answer -(Yes/No)

Answer 1

a)

week	sales	forecast	error	error^2
1	18
2	22
3	20
4	24	20.33	3.67	13.44
5	17	22.33	-5.33	28.44
6	15	19.83	-4.83	23.36
7	19	17.17	1.83	3.36
8	17	17.33	-0.33	0.11
9	23	17.33	5.67	32.11
10	19	20.33	-1.33	1.78
11	14	20.00	-6.00	36.00
12	23	17.17	5.83	34.03
			total	172.64
			average	19.18

b)

MSE =19.18

unweighted moving average as its MSE is smaller

c)

Yes