1. Consider the following time series data Week Value 2 4 18 13 16 17 14 Using t
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Question
1. Consider the following time series data Week Value 2 4 18 13 16 17 14 Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. a. Mean absolute error b. Mean squared error c. Mean absolute percentage error d. What is the forecast for week 7? 2. Refer to the time series data in Exercise 1. Using the average of all the historical data as a forecast for the next period, compute the following measures of forecast accuracy: a. Mean absolute error b. Mean squared errorExplanation / Answer
Sol)
1)
The following table shows the calculations for parts (a), (b), and (c).
Week
Time Series Value
Forecast
Forecast Error
Absolute Value of Forecast Error
Squared Forecast Error
Percentage Error
Absolute Value of Percentage Error
1
18
2
13
18
-5
5
25
-38.46
38.46
3
16
13
3
3
9
18.75
18.75
4
11
16
-5
5
25
-45.45
45.45
5
17
11
6
6
36
35.29
35.29
6
14
17
-3
3
9
-21.43
21.43
Totals
22
104
-51.30
159.38
a. MAE = 22/5 = 4.4
b. MSE = 104/5 = 20.8
c. MAPE = 159.38/5 = 31.88
d. Forecast for week 7 is 14
2)
Week
Time Series Value
Forecast
Forecast Error
Absolute Value of Forecast Error
Squared Forecast Error
Percentage Error
Absolute Value of Percentage Error
1
18
2
13
18.00
-5.00
5.00
25.00
-38.46
38.46
3
16
15.50
0.50
0.50
0.25
3.13
3.13
4
11
15.67
-4.67
4.67
21.81
-42.45
42.45
5
17
14.50
2.50
2.50
6.25
14.71
14.71
6
14
15.00
-1.00
1.00
1.00
-7.14
7.14
Totals
13.67
54.31
-70.21
105.86
a. MAE = 13.67/5 = 2.73
b. MSE = 54.31/5 = 10.86
c. MAPE = 105.89/5 = 21.18
d. Forecast for week 7 is (18 + 13 + 16 + 11 + 17 + 14) / 6 = 14.83
Week
Time Series Value
Forecast
Forecast Error
Absolute Value of Forecast Error
Squared Forecast Error
Percentage Error
Absolute Value of Percentage Error
1
18
2
13
18
-5
5
25
-38.46
38.46
3
16
13
3
3
9
18.75
18.75
4
11
16
-5
5
25
-45.45
45.45
5
17
11
6
6
36
35.29
35.29
6
14
17
-3
3
9
-21.43
21.43
Totals
22
104
-51.30
159.38
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