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Compute the errors of bias and absolute deviation for the forecasts in problem 6 which of the
To compute: The errors of bias and absolute deviation and explain which forecast is the best.
Introduction:
Exponential smoothing:
In exponential smoothing forecast method, older data are given lesser importance, and newer data are given more importance. It is efficient in making short-term forecasts.
Explanation of Solution
Given information:
Forecast for period 1 (F1) = 90
Smoothing constant (α) = 0.1
| Period | Dt |
| 1 | 92 |
| 2 | 127 |
| 3 | 106 |
| 4 | 165 |
| 5 | 125 |
| 6 | 111 |
| 7 | 178 |
| 8 | 97 |
Formula for exponential smoothing:
Calculation of forecast:
The forecast for period 1 is 90.
Period 2:
The forecast for period 2 is 90.2.
Period 3:
The forecast for period 3 is 93.9.
Period 4:
The forecast for period 4 is 95.1.
Period 5:
The forecast for period 5 is 102.1.
Period 6:
The forecast for period 6 is 104.4.
Period 7:
The forecast for period 7 is 105.
Period 8:
The forecast for period 8 is 112.3.
Given information:
Forecast for period 1 (F1) = 90
Smoothing constant (α) = 0.3
| Period | Dt |
| 1 | 92 |
| 2 | 127 |
| 3 | 106 |
| 4 | 165 |
| 5 | 125 |
| 6 | 111 |
| 7 | 178 |
| 8 | 97 |
Calculation of forecast:
The forecast for period 1 is 90.
Period 2:
The forecast for period 2 is 90.6.
Period 3:
The forecast for period 3 is 101.5.
Period 4:
The forecast for period 4 is 102.9.
Period 5:
The forecast for period 5 is 121.5.
Period 6:
The forecast for period 6 is 122.6.
Period 7:
The forecast for period 7 is 119.1.
Period 8:
The forecast for period 8 is 136.8.
Calculation of error and absolute deviation:
For α = 0.1
Excel work:
Excel formula:
For α = 0.3
Excel work:
Excel formula:
For α = 0.1
Sum of error = 208
Sum of absolute deviation = 238.6
For α = 0.3
Sum of error = 116
Sum of absolute deviation = 218.8
The sum of error and absolute deviation is lower for α = 0.3 when compared with values of α = 0.1 (116 < 208) and (218.8 < 238.6). Hence, the forecasting method with α = 0.3 will be the best method.
The forecasting method with α = 0.3 is the best method.
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