Question

1. Compute Three- week and five-week moving averages for the time series. 2. Compute the MSE for Three- week and five-week moving average forecasts. 3. What appears to be the best number of weeks of past data (three or five) to use in the moving average computation? Week Sale (1000s of Gallons) three-week five-week 17 21 19 23 18 16 20 18 10 20 15 12 31 34 31 14 15 16 17 18 19 20 28 32 29 34 21

Answer 1

Excel is attached

1)

week	Value	4-period MA	5-period MA	(Value- 4Period MA)^2	(Value- 5Period MA)^2
1	17
2	21
3	16
4	24
5	17	19.5		6.25
6	18	19.5	19	2.25	1
7	22	18.75	19.2	10.5625	7.84
8	20	20.25	19.4	0.0625	0.36
9	21	19.25	20.2	3.0625	0.64
10	19	20.25	19.6	1.5625	0.36
11	16	20.5	20	20.25	16
12	25	19	19.6	36	29.16
		Total Squared error		80	55.36
	Mean square error		`= sqrt(TSE/n) 8.944272 7.44043

2) MSE of 4-period = 8.944 MSE of 5-period = 7.440

3) MSE of 5-period is lowest. Hence, 5 period of data is the best fit

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