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.
Time Period (t) 1 2

Time Series Value (Y t) 22 26

Exponential (Ft) 22 22

If the smoothing constant equals .3, then the exponential smoothing forecast for time period three is:

A. 28.9
B. 24.8
C. 24.7
D. 21.0
E. 23.2

Answer 1

The exponential smoothing forecast for period three is 24.8.

Step-by-step explanation:

The exponential smoothing forecast for period three can be calculated using the formula:

F(t) = (1 - α) * Y(t-1) + α * F(t-1)

Given that α (the smoothing constant) is 0.3, Y(t-1) is 26, and F(t-1) is 22, we can substitute these values into the formula to find:

F(3) = (1 - 0.3) * 26 + 0.3 * 22

F(3) = 0.7 * 26 + 0.3 * 22

F(3) = 18.2 + 6.6

F(3) = 24.8

Therefore, the exponential smoothing forecast for period three is 24.8 (Option B).