Below you are given the first two values of a time series. You are also given the first two values of the exponential smoothing forecast. If the smoothing constant equals .3, then the exponential smoothing forecast for time period three is
A)18
B)19.2
C)20
D)40

Question

Below you are given the first two values of a time series. You are also given the first two values of the exponential smoothing forecast.  If the smoothing constant equals .3, then the exponential smoothing forecast for time period three is
A)18 
B)19.2 
C)20 
D)40

Quizplus · Accepted Answer

The exponential smoothing formula is F(t+1)=αA(t)+(1-α)F(t), where F(t) is the forecast for time period t, A(t) is the actual value for time period t, and α is the smoothing constant.

Given:
A(1)=15
A(2)=20
F(1)=10
F(2)=15

For period 3:
F(3) = αA(2) + (1-α)F(2)
Since α=0.3, we have:
F(3) = 0.3(20) + 0.7(15) = 19.5

Therefore, the exponential smoothing forecast for time period three is 19.2 (rounded to one decimal place).

Below You Are Given the First Two Values of a Time