Question

Problem 15-07 (Algorithmic)

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

Week	Sales (1000s of gallons)
1	18
2	21
3	18
4	24
5	18
6	15
7	21
8	19
9	22
10	21
11	15
12	23

1. Compute four-week and five-week moving averages for the time series. Round your answers to two decimal places.
   

   Week	Sales	4-Week Moving Average	5-Week Moving Average
   1	18
   2	21
   3	18
   4	24
   5	18
   6	15
   7	21
   8	19
   9	22
   10	21
   11	15
   12	23

2. Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations and final answers to two decimal places.
   
   MSE for four-week moving average =  
   
   MSE for five-week moving average =
   
3. 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 MSE for the three-week moving average is 13.69.
   
   

Answer 1

a.

Week	Sales	4-Week Moving Average: 4w MA	5-week Moving Average: 5w MA
1	18
2	21
3	18
4	24
5	18	(18+21+18+24)/4 =20.25
6	15	(21+18+24+18)/4 =20.25	(18+21+18+24+18)/5 =19.8
7	21	(18+24+18+15)/4 =18.75	(21+18+24+18+15)/5 =19.2
8	19	(24+18+15+21)/4 =19.5	(18+24+18+15+21)/5 =19.2
9	22	(18+15+21+19)/4 =18.25	(24+18+15+21+19)/5 =19.4
10	21	(15+21+19+22)/4 =19.25	(18+15+21+19+22)/5 =19
11	15	(21+19+22+21)/4 =20.75	(15+21+19+22+21)/5 =19.6
12	23	(19+22+21+15)/4 =19.25	(21+19+22+21+15)/5 =19.6

b.

Actual: A	Forecast: F (4w MA)	Error square, E2 =(A - F)2	Forecast:F (5w MA)	Error square, E2 =(A - F)2
18
21
18
24
18	20.25	(18 - 20.25)2 =5.06
15	20.25	27.56	19.8	(15 - 19.8)2 =23.04
21	18.75	5.06	19.2	3.24
19	19.5	0.25	19.2	0.04
22	18.25	14.06	19.4	6.76
21	19.25	3.06	19	4
15	20.75	33.06	19.6	21.16
23	19.25	14.06	19.6	11.56
Total		=102.17		=69.8

MSE for four-week moving average =  /n =102.17/8 =12.77

MSE for five-week moving average =/n =69.8/7 =9.97

c.

MSE for three-week moving average =13.69

MSE for four-week moving average =12.77

MSE for five-week moving average =9.97

Since MSE for five-week moving average is the smallest of the three, five weeks appear to be the best number of weeks of past data to use in the moving average computation.