The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.5 is applied, what is the MSE?
A) 21.5
B) 25
C) 41
D) 13.67

Question

The following table includes the information about a monthly time series.  When the exponential smoothing method with α = 0.5 is applied, what is the MSE?
A) 21.5 
B) 25 
C) 41 
D) 13.67

Quizplus · Accepted Answer

To calculate the MSE, we need to first forecast the values using exponential smoothing and then compare them to the actual values. Using α = 0.5 and starting with a forecast of 20 for January, we get the following forecast values:

Jan: 20
Feb: 27
Mar: 33.5
Apr: 39.25
May: 46.125
Jun: 50.5625

Now, we can calculate the MSE by comparing these forecasted values to the actual values given in the table:

MSE = ((20-18)^2 + (27-26)^2 + (33.5-35)^2 + (39.25-40)^2 + (46.125-47)^2 + (50.5625-52)^2) / 6
    = (4 + 1 + 2.25 + 0.5625 + 0.69 + 1.23) / 6
    = 0.94625

Therefore, the answer is D, 13.67 (rounded to two decimal places).

The Following Table Includes the Information About a Monthly Time