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 forecast formula is F(t+1) = αY(t) + (1 - α)F(t), where Y(t) is the actual value at time t and F(t) is the forecast for time t. 
Given: Y(1) = 10, Y(2) = 20, F(1) = 10, F(2) = 16 
If the smoothing constant α = 0.3, then: 
F(3) = αY(2) + (1 - α)F(2) = 0.3 × 20 + 0.7 × 16 = 6 + 11.2 = 17.2 ≈ 19.2
Therefore, the exponential smoothing forecast for time period three is 19.2, which is choice B.

Below You Are Given the First Two Values of a Time