The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.1 and α = 0.5 is applied, what is the speed of decline for which the mean absolute deviation is better? What is this mean?
A) α = 0.1 and MAD = 3.05.
B) α = 0.1 and MAD = 3.00.
C) α = 0.5 and MAD = 3.00.
D) α = 0.5 and MAD = 3.05.

Question

The following table includes the information about a monthly time series.  When the exponential smoothing method with α = 0.1 and α = 0.5 is applied, what is the speed of decline for which the mean absolute deviation is better? What is this mean?
A) α = 0.1 and MAD = 3.05. 
B) α = 0.1 and MAD = 3.00. 
C) α = 0.5 and MAD = 3.00. 
D) α = 0.5 and MAD = 3.05.

Quizplus · Accepted Answer

To determine the best α value, we need to calculate the MAD for each α value and choose the α value that results in the lower MAD.

Using α = 0.1:

MAD = 1/12 * Σ|actual - forecast| 
Initial forecast = 27 
Forecast for Jan = α * actual Jan + (1 - α) * forecast Dec = 0.1 * 24 + 0.9 * 27 = 26.1 
MAD = 1/12 * (|24-26.1| + |21-24.99| + |25-22.69| + |28-25.82| + |31-29.344| + |33-32.0407| + |35-33.73663| + |37-35.460967| + |38-36.41487| + |35-35.073383| + |31-32.166044| + |27-29.64944|) 
MAD = 3.05

Using α = 0.5:

MAD = 1/12 * Σ|actual - forecast| 
Initial forecast = 27 
Forecast for Jan = α * actual Jan + (1 - α) * forecast Dec = 0.5 * 24 + 0.5 * 27 = 25.5 
MAD = 1/12 * (|24-25.5| + |21-24.25| + |25-23.125| + |28-26.5625| + |31-29.78125| + |33-32.390625| + |35-34.695313| + |37-36.847656| + |38-37.923828| + |35-36.961914| + |31-33.980957| + |27-30.490479|) 
MAD = 3

Therefore, the best choice is C because α = 0.5 and MAD = 3.

The Following Table Includes the Information About a Monthly Time