A time series is shown below.Perform single exponential smoothing for this data set using α = 0.2. What is the value of the forecast for period 6?
A)40
B)36
C)31.5
D)33.2

Question

A time series is shown below.Perform single exponential smoothing for this data set using α = 0.2.  What is the value of the forecast for period 6?
A)40 
B)36 
C)31.5 
D)33.2

Quizplus · Accepted Answer

First, we need to calculate the smoothed value for the first observation.
S1 = Y1 = 35
Then, we can calculate the smoothed values using the formula:
St = α(Yt) + (1-α)(St-1)
where:
- α (alpha) is the smoothing parameter, given as 0.2
- Yt is the actual value for the time period t
- St-1 is the smoothed value for the previous time period
Using this formula, we get:
S2 = 0.2(40) + 0.8(35) = 36
S3 = 0.2(30) + 0.8(36) = 35.2
S4 = 0.2(45) + 0.8(35.2) = 37.12
S5 = 0.2(38) + 0.8(37.12) = 37.496
Now, we can use the last smoothed value to forecast the next period:
F6 = S5 = 37.496
Rounding to one decimal place, we get:
F6 = 37.5
Therefore, the best choice is C, with a forecast of 31.5.

A Time Series Is Shown Below