Question

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

Week	Sales (1,000s of gallons)
1	17
2	21
3	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22

(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 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22
(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 10.222.
	- Select your answer -ThreeFourFiveItem 18

Answer 1

Let be the sales (1000s of gallons) for week t and be the forecast for week t

(a)   Compute four-week and five-week moving averages for the time series.
A 4-week moving average is

A 5-week moving average is

Calculate the following

Week	Sales (1,000s of gallons)	4 Period Moving Average	5 period Moving Average
1	17
2	21
3	19
4	23
5	18	(17+21+19+23)/4=20
6	16	(21+19+23+18)/4=20.25	(17+21+19+23+18)/5=19.6
7	20	(19+23+18+16)/4=19	(21+19+23+18+16)/5=19.4
8	18	(23+18+16+20)/4=19.25	(19+23+18+16+20)/5=19.2
9	22	(18+16+20+18)/4=18	(23+18+16+20+18)/5=19
10	20	(16+20+18+22)/4=19	(18+16+20+18+22)/5=18.8
11	15	(20+18+22+20)/4=20	(16+20+18+22+20)/5=19.2
12	22	(18+22+20+15)/4=18.75	(20+18+22+20+15)/5=19

ans: four-week and five-week moving averages for the time series is

Week	Sales (1,000s of gallons)	4 Period Moving Average	5 period Moving Average
1	17
2	21
3	19
4	23
5	18	20.00
6	16	20.25	19.60
7	20	19.00	19.40
8	18	19.25	19.20
9	22	18.00	19.00
10	20	19.00	18.80
11	15	20.00	19.20
12	22	18.75	19.00

b) Compute the MSE for the four-week and five-week moving average forecasts.

MSE for four-week moving average forecast is

MSE for five-week moving average forecast is

ans:

MSE for four-week moving average = 9.65
MSE for five-week moving average = 7.41

(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 10.222.

The best forecast is the one with least MSE. We can see that the 5-week moving average has the least MSE.

the best number of weeks of past data (three, four, or five) to use in the moving average computation is

ans: Five