Consider the time series data given below a. Using the naïve forecasting method
ID: 3369653 • Letter: C
Question
Consider the time series data given below
a. Using the naïve forecasting method to forecast the value of the next week. Compute the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE).
b. Using the average forecasting method to forecast the value of the next week. Compute the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE).
c. Using the moving average forecast of order 3 to forecast the value of the next week. Compute the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE).
d. Using the weighted moving average forecast of order 3 to forecast the value of the next week. The weights are 1/6, 2/6, and 3/6, respectively.Compute the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE)
e. Using the exponential smoothing forecasting method to forecast the value of the next week. Set alpha = 0.7.Compute the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE).
week value 1 18 2 13 3 16 4 11 5 17 6 14Explanation / Answer
Solutions:
a. The following table shows the calculations
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
1. MAE = 22/5 = 4.4
2. MSE = 104/5 = 20.8
3. MAPE = 159.38/5 = 31.88
4. Forecast for week 7 is 14
b. The following table shows the calculations
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
1. MAE = 13.67/5 = 2.73
2. MSE = 54.31/5 = 10.86
3. MAPE = 105.89/5 = 21.18
4. Forecast for week 7 is (18 + 13 + 16 + 11 + 17 + 14) / 6 = 14.83
c.
1. MAE = 9/3 = 3
2. MSE = 35.67/3 = 11.89
3. MAPE = 64.048/3 = 21.35
4. Forecast for week 7 is 14
d.
1. MAE = 9/3 = 3
2. MSE = 35.67/3 = 11.89
3. MAPE = 64.048/3 = 21.35
4. Forecast for week 7 is 14
e.
1. MAE = 10.79/5 = 2.16
2. MSE = 44.78/5 = 8.96
3. MAPE = 80.12/5 = 26.71
4. Forecast for week 7 is 14.48
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