Question

Problem 15-07 (Algorithmic)

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

Week	Sales (1000s of gallons)
1	17
2	21
3	19
4	24
5	18
6	15
7	21
8	19
9	22
10	21
11	16
12	22

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	17
   2	21
   3	19
   4	24
   5	18
   6	15
   7	21
   8	19
   9	22
   10	21
   11	16
   12	22

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 12.26.
   
   

Answer 1

a)

from above

			4 period	5 period
week	sales		forecast	forecast
1	17
2	21
3	19
4	24
5	18		20.25
6	15		20.50	19.8
7	21		19.00	19.4
8	19		19.50	19.4
9	22.00		18.25	19.4
10	21.00		19.25	19
11	16.00		20.75	19.6
12	22.00		19.50	19.80

b)

4 period	5 period
MSE	MSE
5.06
30.25	23.04
4.00	2.56
0.25	0.16
14.06	6.76
3.06	4.00
22.56	12.96
6.25	4.84
total =10.69	7.76

MSE for four-week moving average = 10.69

MSE for five-week moving average = 7.76

c)

five week moving average apepars to be better due to smallest MSE