Question

Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.

Week	Sales (1,000s of gallons)
1	21
2	25
3	23
4	27
5	22
6	20
7	24
8	22
9	26
10	24
11	19
12	26

Show the exponential smoothing forecasts using α = 0.1. (Round your answers to two decimal places.)

Week	Time Series Value	Forecast
1	21
2	25
3	23
4	27
5	22
6	20
7	24
8	22
9	26
10	24
11	19
12	26

(a)

Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of

α = 0.1

or

α = 0.2

for the gasoline sales time series?

α = 0.1 provides more accurate forecasts based upon MSE.α = 0.2 provides more accurate forecasts based upon MSE.    Both provide the same level of accuracy of forecasts based upon MSE.

(b)

Are the results the same if you apply MAE as the measure of accuracy?

α = 0.1 provides more accurate forecasts based upon MAE, so the results are the same.α = 0.1 provides more accurate forecasts based upon MAE, so the results are not the same.    α = 0.2 provides more accurate forecasts based upon MAE, so the results are the same.α = 0.2 provides more accurate forecasts based upon MAE, so the results are not the same.Both provide the same level of accuracy based on MAE, so the results are the same.Both provide the same level of accuracy based on MAE, so the results are not the same.

(c)

What are the results if MAPE is used?

α = 0.1 provides more accurate forecasts based upon MAPE.α = 0.2 provides more accurate forecasts based upon MAPE.    Both provide the same level of accuracy of forecasts based upon MAPE.

Answer 1

For alpha = 0.1, the results are -

Week	Time series value	Forecast
1	21	23.00
2	25	22.80
3	23	23.02
4	27	23.02
5	22	23.42
6	20	23.27
7	24	22.95
8	22	23.05
9	26	22.95
10	24	23.25
11	19	23.33
12	26	22.89

(a) α MSE

0.1 6.49

0.2 7.14

α = 0.1 provides more accurate forecasts based upon MSE..

(b) α MAE

0.1 2.18

0.2 2.30

α = 0.1 provides more accurate forecasts based upon MAE, so the results are not the same.

(c) α   MAPE

0.1 9.55

0.2 10.08

From above information α = 0.1 provides most accurate forecasts based upon MAPE.