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 .2, then the exponential smoothing forecast for time period 3 is
A) 18.
B) 18.8.
C) 21.2.
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 .2, then the exponential smoothing forecast for time period 3 is
A) 18. 
B) 18.8. 
C) 21.2. 
D) 40.

Quizplus · Accepted Answer

Exponential smoothing formula: 
Forecast for time (t+1) = α(actual value at t) + (1-α) (Forecast for time t)

Given:
α = 0.2
Actual value at time 1 = 10
Forecast for time 1 = 12
Actual value at time 2 = 18
Forecast for time 2 = 12.4

Forecast for time 3: 
= α(actual value at time 2) + (1-α) (Forecast for time 2)
= 0.2(18) + 0.8(12.4)
= 3.6 + 9.92
= 13.52

Therefore, the exponential smoothing forecast for time period 3 is 13.52, which corresponds to answer choice B.

Below You Are Given the First Two Values of a Time