Question

Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits.

Week	Sales (1,000s of gallons)
1	17
2	21
3	16
4	24
5	17
6	18
7	22
8	20
9	21
10	19
11	16
12	25

(a)	Show the exponential smoothing forecasts using α = 0.1, and α = 0.2.
	Exponential Smoothing Week α = 0.1 α = 0.2 13
(b)	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?
	An - Select your answer -α = 0.1α = 0.2Item 3 smoothing constant provides the more accurate forecast, with an overall MSE of  .
(c)	Are the results the same if you apply MAE as the measure of accuracy?
	An - Select your answer -α = 0.1α = 0.2Item 5 smoothing constant provides the more accurate forecast, with an overall MAE of  .
(d)	What are the results if MAPE is used?
	An - Select your answer -α = 0.1α = 0.2Item 7 smoothing constant provides the more accurate forecast, with an overall MAPE of  .

Answer 1

Answer a)

Thus, Week 13 Forecast for α = 0.1 is 19.1109

Thus, Week 13 Forecast for α = 0.2 is 20.0254

Following table that shows the calculations error metrics (α = 0.1):

Following table that shows the calculations error metrics (α = 0.2):

Answer b)

Based on error metrics table, it can be seen that:

MSE (α = 0.1) = (0+16+1.96+45.4276+0.8724+0.0254+17.1683+2.9898+6.5342+0.0903+7.45+42.817)/12

MSE (α = 0.1) = 11.78

MSE (α = 0.2) = (0+16+3.24+43.0336+3.0695+0.1613+13.533+0.8892+3.0779+0.3558+12.0909+38.6665)/12

MSE (α = 0.2) = 11.18

Thus, α = 0.2 smoothing constant provides the more accurate forecast, with an overall MSE of 11.18

Answer c)

Based on error metrics table, it can be seen that:

MAE (α = 0.1) = (0+4+1.4+6.74+0.934+0.1594+4.1435+1.7291+2.5562+0.3006+2.7295+6.5435)/12

MAE (α = 0.1) = 2.6030

MAE (α = 0.2) = (0+4+1.8+6.56+1.752+0.4016+3.6787+0.943+1.7544+0.5965+3.4772+6.2182)/12

MAE (α = 0.2) = 2.5985

Thus, α = 0.2 smoothing constant provides the more accurate forecast, with an overall MAE of 2.5985

Answer d)

MAPE (α = 0.1) = (0+19.05+8.75+28.08+5.49+0.89+18.83+8.65+12.17+1.58+17.06+26.17)/12 = 12.23%

MAPE (α = 0.2) = (0+19.05+11.25+27.33+10.31+2.23+16.72+4.71+8.35+3.14+21.73+24.87)/12 = 12.48%

Thus, α = 0.1 smoothing constant provides the more accurate forecast, with an overall MAPE of 12.23%