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 value of alpha for exponential smoothing, we need to calculate the Mean Absolute Deviation (MAD) for both values of alpha, 0.1 and 0.5.

Using alpha = 0.1: 
The initial forecast for January is 160. Applying exponential smoothing, we get the following forecasts:

F(1) = αD(1) + (1-α)F(0) = 0.1(190) + 0.9(160) = 163 
F(2) = αD(2) + (1-α)F(1) = 0.1(-20) + 0.9(163) = 147.7 
F(3) = αD(3) + (1-α)F(2) = 0.1(25) + 0.9(147.7) = 153.5 
F(4) = αD(4) + (1-α)F(3) = 0.1(-15) + 0.9(153.5) = 138.8 
F(5) = αD(5) + (1-α)F(4) = 0.1(5) + 0.9(138.8) = 140.9 
F(6) = αD(6) + (1-α)F(5) = 0.1(10) + 0.9(140.9) = 142.8

The MAD for alpha = 0.1 is: 
MAD = (|190-163| + |-20-147.7| + |25-153.5| + |-15-138.8| + |5-140.9| + |10-142.8|)/6 = 3.05

Using alpha = 0.5: 
The initial forecast for January is 160. Applying exponential smoothing, we get the following forecasts:

F(1) = αD(1) + (1-α)F(0) = 0.5(190) + 0.5(160) = 175 
F(2) = αD(2) + (1-α)F(1) = 0.5(-20) + 0.5(175) = 77.5 
F(3) = αD(3) + (1-α)F(2) = 0.5(25) + 0.5(77.5) = 51.2 
F(4) = αD(4) + (1-α)F(3) = 0.5(-15) + 0.5(51.2) = 18.6 
F(5) = αD(5) + (1-α)F(4) = 0.5(5) + 0.5(18.6) = 11.8 
F(6) = αD(6) + (1-α)F(5) = 0.5(10) + 0.5(11.8) = 10.9

The MAD for alpha = 0.5 is: 
MAD = (|190-175| + |-20-77.5| + |25-51.2| + |-15-18.6| + |5-11.8| + |10-10.9|)/6 = 3.00

Since the MAD is better (lower) for alpha = 0.5, the answer is (C) alpha = 0.5 and MAD = 3.00.

The Following Table Includes the Information About a Monthly Time