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	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22

(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 = 0.1 / α = 0.2 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 = 0.1 / α = 0.2 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 = 0.2 smoothing constant provides the more accurate forecast, with an overall MAPE of  .

Answer 1

Exponential smoothing (α=0.1)

Week	Sales (1,000s of gallons)(Y)	Y^ = ES(0.1) = αAt+(1-α)Ft	ABS Error = |Y-Y^|	Error^2	Absolute % error = ABS error/Y
1	17	17	0	0	0.00%
2	21	17	4	16	19.05%
3	19	17.4	1.6	2.56	8.42%
4	23	17.56	5.44	29.5936	23.65%
5	18	18.104	0.104	0.010816	0.58%
6	16	18.0936	2.0936	4.383161	13.09%
7	20	17.88424	2.11576	4.47644	10.58%
8	18	18.095816	0.095816	0.009181	0.53%
9	22	18.0862344	3.9137656	15.31756	17.79%
10	20	18.47761096	1.52238904	2.317668	7.61%
11	15	18.62984986	3.629849864	13.17581	24.20%
12	22	18.26686488	3.733135122	13.9363	16.97%
13		18.64017839
		Average	2.3540	8.4817	11.87%

Exponential smoothing (α=0.2)

Week	Sales (1,000s of gallons)(Y)	Y^ = ES(0.2) = αAt+(1-α)Ft	ABS Error = |Y-Y^|	Error^2	Absolute % error = ABS error/Y
1	17	17	0	0	0.00%
2	21	17	4	16	19.05%
3	19	17.8	1.2	1.44	6.32%
4	23	18.04	4.96	24.6016	21.57%
5	18	19.032	1.032	1.065024	5.73%
6	16	18.8256	2.8256	7.9840154	17.66%
7	20	18.26048	1.73952	3.0259298	8.70%
8	18	18.608384	0.608384	0.3701311	3.38%
9	22	18.4867072	3.5132928	12.343226	15.97%
10	20	19.18936576	0.81063424	0.6571279	4.05%
11	15	19.35149261	4.351492608	18.935488	29.01%
12	22	18.48119409	3.518805914	12.381995	15.99%
13		19.18495527
		Average	2.3800	8.2337	12.29%

a)

	Exponential
	Smoothing
Week	α = 0.1	α = 0.2
13	18.6402	19.185

b)

	Exponential
	Smoothing
	α = 0.1	α = 0.2
MSE	8.4817	8.2337

MSE(α = 0.2) < MSE(α = 0.1)

An α = 0.2 smoothing constant provides the more accurate forecast, with an overall MSE of 8.2337

c)

	Exponential
	Smoothing
	α = 0.1	α = 0.2
MAE	2.354	2.38

MAE(α = 0.2) > MAE(α = 0.1)

An α = 0.1 smoothing constant provides the more accurate forecast, with an overall MAE of 2.354

d)

	Exponential
	Smoothing
	α = 0.1	α = 0.2
MAPE	11.87%	12.29%

An α = 0.1 smoothing constant provides the more accurate forecast, with an overall MAPE of 11.87%

MAPE(α = 0.2) > MAPE(α = 0.1)