(a)
Obtain exponential smoothing for
Identify the preferred smoothing constant using MSE measure of forecast accuracy.
(a)
Explanation of Solution
Exponential smoothing for
Exponential smoothing is obtained using the formula given below:
Week | Time Series Value | Forecast | Forecast Error | Squared Forecast Error |
1 | 17 | |||
2 | 21 | 4.00 | 16.00 | |
3 | 19 | 1.60 | 2.56 | |
4 | 23 | 5.44 | 29.59 | |
5 | 18 | −0.10 | 0.01 | |
6 | 16 | −2.09 | 4.38 | |
7 | 20 | 2.12 | 4.48 | |
8 | 18 | −0.10 | 0.01 | |
9 | 22 | 3.91 | 15.32 | |
10 | 20 | 1.52 | 2.32 | |
11 | 15 | −3.63 | 13.18 | |
12 | 22 | 3.73 | 13.94 | |
Total | 101.78 |
Thus, the mean squared error is 9.253.
Exponential smoothing for
Week | Time Series Value | Forecast | Forecast Error | Squared Forecast Error |
1 | 17 | |||
2 | 21 | 4.00 | 16.00 | |
3 | 19 | 1.20 | 1.44 | |
4 | 23 | 4.96 | 24.60 | |
5 | 18 | −1.03 | 1.07 | |
6 | 16 | −2.83 | 7.98 | |
7 | 20 | 1.74 | 3.03 | |
8 | 18 | −0.61 | 0.37 | |
9 | 22 | 3.51 | 12.34 | |
10 | 20 | 0.81 | 0.66 | |
11 | 15 | −4.35 | 18.94 | |
12 | 22 | 3.52 | 12.38 | |
Total | 98.80 |
Thus, the mean squared error is 8.982.
MSE when
(b)
Check whether the results are same when MAE is used as measure of accuracy.
(b)
Answer to Problem 8P
No, the results are not same.
Explanation of Solution
The MSE for four-week moving average is obtained as given below:
Exponential smoothing for
Exponential smoothing is obtained using the formula given below:
Week | Time Series Value | Forecast | Forecast Error | Absolute Forecast Error |
1 | 17 | |||
2 | 21 | 4.00 | 4.00 | |
3 | 19 | 1.60 | 1.60 | |
4 | 23 | 5.44 | 5.44 | |
5 | 18 | −0.10 | 0.10 | |
6 | 16 | −2.09 | 2.09 | |
7 | 20 | 2.12 | 2.12 | |
8 | 18 | −0.10 | 0.10 | |
9 | 22 | 3.91 | 3.91 | |
10 | 20 | 1.52 | 1.52 | |
11 | 15 | −3.63 | 3.63 | |
12 | 22 | 3.73 | 3.73 | |
Total | 28.25 |
Thus, the mean absolute error is 2.568.
Exponential smoothing for
Week | Time Series Value | Forecast | Forecast Error | Squared Forecast Error |
1 | 17 | |||
2 | 21 | 4.00 | 4.00 | |
3 | 19 | 1.20 | 1.20 | |
4 | 23 | 4.96 | 4.96 | |
5 | 18 | −1.03 | 1.03 | |
6 | 16 | −2.83 | 2.83 | |
7 | 20 | 1.74 | 1.74 | |
8 | 18 | −0.61 | 0.61 | |
9 | 22 | 3.51 | 3.51 | |
10 | 20 | 0.81 | 0.81 | |
11 | 15 | −4.35 | 4.35 | |
12 | 22 | 3.52 | 3.52 | |
Total | 28.56 |
Thus, the mean absolute error is 2.596.
MAE when
Hence, the results are not same when MAE is used as measure of accuracy.
(c)
Obtain the results when MAPE is used as measure of accuracy.
(c)
Answer to Problem 8P
MAPE when
MAPE when
Explanation of Solution
Exponential smoothing for
Week | Time Series Value | Forecast | Forecast Error | |
1 | 17 | |||
2 | 21 | 4.00 | 19.05 | |
3 | 19 | 1.60 | 8.42 | |
4 | 23 | 5.44 | 23.65 | |
5 | 18 | −0.10 | 0.58 | |
6 | 16 | −2.09 | 13.09 | |
7 | 20 | 2.12 | 10.58 | |
8 | 18 | −0.10 | 0.53 | |
9 | 22 | 3.91 | 17.79 | |
10 | 20 | 1.52 | 7.61 | |
11 | 15 | −3.63 | 24.20 | |
12 | 22 | 3.73 | 16.97 | |
Total | 142.46 |
Thus, the value of MAPE is 12.95.
Exponential smoothing for
Week | Time Series Value | Forecast | Forecast Error | |
1 | 17 | |||
2 | 21 | 4.00 | 19.05 | |
3 | 19 | 1.20 | 6.32 | |
4 | 23 | 4.96 | 21.57 | |
5 | 18 | −1.03 | 5.73 | |
6 | 16 | −2.83 | 17.66 | |
7 | 20 | 1.74 | 8.70 | |
8 | 18 | −0.61 | 3.38 | |
9 | 22 | 3.51 | 15.97 | |
10 | 20 | 0.81 | 4.05 | |
11 | 15 | −4.35 | 29.01 | |
12 | 22 | 3.52 | 15.99 | |
Total | 147.43 |
Thus, the value of MAPE is 13.40.
MAPE when
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Chapter 5 Solutions
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