Problem 15-08 (Algorithmic) Refer again to the gasoline sales time series data i
ID: 372028 • Letter: P
Question
Problem 15-08 (Algorithmic)
Refer again to the gasoline sales time series data in the following table.
Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. Use rounded for two decimal places values for intermediate colculations.
Compute the MSE for the weighted moving average in part a. Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 10.22. Round your answer to two decimal places.
MSE =
Prefer the moving average here.
Explanation / Answer
Below table calculates sum of Error^2 for all 12 weeks which is 192.08:
WEEK
SALES
WEIGHTED MOVING AVERAGE FORECAST
FORECAST ERROR = SALES - FORECAST
ERROR^2
1
16
2
22
3
21
4
26
20.50
5.50
30.25
5
19
23.67
-4.67
21.78
6
14
21.67
-7.67
58.78
7
21
17.67
3.33
11.11
8
18
18.33
-0.33
0.11
9
23
18.33
4.67
21.78
10
23
21.00
2.00
4.00
11
16
22.17
-6.17
38.03
12
22
19.50
2.50
6.25
TOTAL =
TOTAL :
192.08
Therefore , Mean Squared error ( MSE ) = 192.08/12 = 16.00 ( rounded to 2 decimal places)
Given , MSE for unweighted moving average = 10.22
A Lower MSE is always preferable since it indicates lesser difference between actual and forecast value.
Therefore , WE PREFER THE UNWEIGHTED MOVING AVERAGE
WEEK
SALES
WEIGHTED MOVING AVERAGE FORECAST
FORECAST ERROR = SALES - FORECAST
ERROR^2
1
16
2
22
3
21
4
26
20.50
5.50
30.25
5
19
23.67
-4.67
21.78
6
14
21.67
-7.67
58.78
7
21
17.67
3.33
11.11
8
18
18.33
-0.33
0.11
9
23
18.33
4.67
21.78
10
23
21.00
2.00
4.00
11
16
22.17
-6.17
38.03
12
22
19.50
2.50
6.25
TOTAL =
TOTAL :
192.08