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

To calculate the MAD using exponential smoothing:
1. Calculate the smoothed values using exponential smoothing with α = 0.1.
2. Calculate the forecast errors by subtracting the actual values from the smoothed values.
3. Calculate the absolute values of the forecast errors.
4. Calculate the average of the absolute forecast errors.

Using the formula for exponential smoothing, we can calculate the smoothed values as follows:
S1 = 54
S2 = 0.1 * 57 + 0.9 * 54 = 54.3
S3 = 0.1 * 62 + 0.9 * 54.3 = 55.17
S4 = 0.1 * 59 + 0.9 * 55.17 = 55.40
S5 = 0.1 * 79 + 0.9 * 55.40 = 63.46
S6 = 0.1 * 84 + 0.9 * 63.46 = 71.06

The forecast errors are:
e1 = 54 - 57 = -3
e2 = 57 - 62 = -5
e3 = 62 - 59 = 3
e4 = 59 - 79 = -20
e5 = 79 - 84 = -5
e6 = 84 - 76 = 8

The absolute forecast errors are:
|e1| = 3
|e2| = 5
|e3| = 3
|e4| = 20
|e5| = 5
|e6| = 8

The average of the absolute forecast errors is:
MAD = (3 + 5 + 3 + 20 + 5 + 8) / 6 = 3.05

Therefore, the answer is C) 3.05.

The Following Table Includes the Information About a Monthly Time