Question

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

Click on the datafile logo to reference the data.

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 intermediate calculations to four decimal places and 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? Recall that the MSE for the three-week moving average is 10.22.
	- Select your answer -3, 4, OR 5

Answer 1

(a)

Let shows the value of current year t. So 4 -week moving average can be calcualted as follow:

and formula for 5-week moving average is

Following table shows the moving average :

Week	Sales (1,000s of gallons)	Four year moving average	Five year moving average
1	17
2	21
3	19
4	23
5	18	20
6	16	20.25	19.6
7	20	19	19.4
8	18	19.25	19.2
9	22	18	19
10	20	19	18.8
11	15	20	19.2
12	22	18.75	19

(b)

For four week moving average:

Week	Sales (1,000s of gallons), Yt	Four year moving average,Ft	(Yt-Ft)^2
1	17
2	21
3	19
4	23
5	18	20	4
6	16	20.25	18.0625
7	20	19	1
8	18	19.25	1.5625
9	22	18	16
10	20	19	1
11	15	20	25
12	22	18.75	10.5625
Total			77.1875

So

For five week moving average:

Week	Sales (1,000s of gallons), Yt	Five year moving average, Ft	(Yt-Ft)^2
1	17
2	21
3	19
4	23
5	18
6	16	19.6	12.96
7	20	19.4	0.36
8	18	19.2	1.44
9	22	19	9
10	20	18.8	1.44
11	15	19.2	17.64
12	22	19	9
Total			51.84

So

(c)

Five week moving average has smallest MSE so it is best to use.