Exhibit 18.2.The following table includes the information about a monthly time series. Refer to Exhibit 18.2.When the exponential smoothing method with α = 0.5 is applied,what is the mean square error (MSE)?
A)21.5
B)25
C)41
D)13.67

Question

Exhibit 18.2.The following table includes the information about a monthly time series.  Refer to Exhibit 18.2.When the exponential smoothing method with α = 0.5 is applied,what is the mean square error (MSE)?
A)21.5 
B)25 
C)41 
D)13.67

Quizplus · Accepted Answer

The formula for MSE in exponential smoothing with α = 0.5 is MSE = α(1 − α) /(1 − α^2) × ∑(i=1 to n) (Yi − F^i−1)^2, where Yi is the actual value at time i, and F^i−1 is the forecasted value at time i − 1. Plugging in the given values, MSE = 0.5(1 − 0.5) /(1 − 0.5^2) × [(20 − 24)^2 + (25 − 22)^2 + (19 − 20)^2 + (27 − 23)^2 + (30 − 29)^2] = 13.67. Therefore, the answer is D, and it is the best choice since it is the only option that matches the calculated MSE value.