Question

Refer to the gasoline sales time series data in the given table.

Week	Sales (1,000s of gallons)
1	17
2	21
3	16
4	24
5	17
6	18
7	22
8	20
9	21
10	19
11	16
12	25

(a)	Compute four-week and five-week moving averages for the time series.
	If required, round your answers to two decimal places.
	Week Sales 4 Period Moving Average 5 period Moving Average 1 17 2 21 3 16 4 24 5 17 6 18 7 22 8 20 9 21 10 19 11 16 12 25
(b)	Compute the MSE for the four-week and five-week moving average forecasts.
	If required, round your final answers to three decimal places.
	MSE for four-week moving average =
	MSE for five-week moving average =
(c)	What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Consider that the MSE for the three-week moving average is 12.852.
	- Select your answer -ThreeFourFiveItem 18

Answer 1

Given data,

Week	Sales (1,000s of gallons)
1	17
2	21
3	16
4	24
5	17
6	18
7	22
8	20
9	21
10	19
11	16
12	25

Solution:

a) Computing 4-week and 5-week Moving averages.

• 4- Period Moving Average = Sum up the four consective year and divide by 4.
• 5- Period Moving Average = Sum up the five consective year and divide by 5.

Week	Sales (1,000s of gallons)	4 Period Moving Average	5 period Moving Average
1	17	-	-
2	21	-	-
3	16	-	-
4	24	-	-
5	17	(17+21+16+24)/4	-
6	18	(21+16+24+17)/4	(17+21+16+24+17)/5
7	22	(16+24+17+18)/4	(21+16+24+17+18)/5
8	20	(24+17+18+22)/4	(16+24+17+18+22)/5
9	21	(17+18+22+20)/4	(24+17+18+22+20)/5
10	19	(18+22+20+21)/4	(17+18+22+20+21)/5
11	16	(22+20+21+19)/4	(18+22+20+21+19)/5
12	25	(20+21+19+16)/4	(22+20+21+19+16)/5

Result:

Week	Sales (1,000s of gallons)	4 Period Moving Average	5 period Moving Average
1	17	-	-
2	21	-	-
3	16	-	-
4	24	-	-
5	17	20.25	-
6	18	19.50	19.00
7	22	18.75	19.20
8	20	20.25	19.40
9	21	19.25	20.20
10	19	20.25	19.6
11	16	20.50	20
12	25	19.00	19.6

b)

Week	Sales (1,000s of gallons)	4 Period Moving Average	Error	(Error)^2	5 period Moving Average	Error	(Error)^2
1	17	-	-	-	-	-	-
2	21	-	-	-	-	-	-
3	16	-	-	-	-	-	-
4	24	-	-	-	-	-	-
5	17	20.25	-3.25	10.5625	-	-	-
6	18	19.50	-1.5	2.2500	19.00	-1.00	1.0000
7	22	18.75	3.25	12.2500	19.20	2.80	7.8400
8	20	20.25	-0.25	0.0625	19.40	0.60	0.3600
9	21	19.25	1.75	3.0625	20.20	0.80	0.6400
10	19	20.25	-1.25	1.5625	19.6	-0.60	0.3600
11	16	20.50	-4.50	20.25	20	-4.00	16.0000
12	25	19.00	6.00	36	19.6	5.40	29.1600
Total				86			55.36

     

MSE for 4-week moving average = 86/8 = 10.75

MSE for 5-week moving average = 55.36/7 = 7.91

c) It is preferred to choose lowest MSE for training and highest MSE for testing.

Five week moving average.