The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.1 is applied, what is the MAD?
A) 20.796
B) 9.16
C) 3.05
D) 3.56

Question

The following table includes the information about a monthly time series.  When the exponential smoothing method with α = 0.1 is applied, what is the MAD?
A) 20.796 
B) 9.16 
C) 3.05 
D) 3.56

Quizplus · Accepted Answer

Using exponential smoothing with α = 0.1, the forecast for the first month is 131. The forecast for the second month is a weighted average of the forecast for the first month and the actual value of the first month: 0.1(131) + 0.9(125) = 125.6. Continuing in this way, we obtain the following table:

| Month | Actual Value | Forecast | Error | Absolute Error |
|-------|-------------|----------|-------|----------------|
|  1    |   125       |  131     |  -6   |       6        |
|  2    |   145       | 125.6    |  19.4 |      19.4      |
|  3    |   155       | 129.64   |  25.4 |      25.4      |
|  4    |   140       | 137.676  |   2.3 |       2.3      |
|  5    |   160       | 140.908  |  19.1 |      19.1      |
|  6    |   160       | 150.017  |   9.9 |       9.9      |
|  7    |   180       | 160.915  |  19.1 |      19.1      |
|  8    |   175       | 170.523  |   4.5 |       4.5      |
|  9    |   190       | 176.67   |  13.3 |      13.3      |
|  10   |   200       | 189.003  |  11.0 |      11.0      |
|  11   |   210       | 195.903  |  14.1 |      14.1      |

The MAD is the mean of the absolute errors, which is (6+19.4+25.4+2.3+19.1+9.9+19.1+4.5+13.3+11+14.1)/11 = 9.1636. Thus, the answer is C.

The Following Table Includes the Information About a Monthly Time