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

a)

	α=	0.1		Exponential smoothing
period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error	Abs %error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²	| et/Dt |
1	17
2	21	17	4.00	4.00	16.0	19.05%
3	16	17.4	-1.40	1.40	2.0	8.75%
4	24	17.26	6.74	6.74	45.4	28.08%
5	17	17.934	-0.93	0.93	0.9	5.49%
6	18	17.8406	0.16	0.16	0.0	0.89%
7	22	17.85654	4.14	4.14	17.2	18.83%
8	20	18.270886	1.73	1.73	3.0	8.65%
9	21	18.4437974	2.56	2.56	6.5	12.17%
10	19	18.6994177	0.30	0.30	0.1	1.58%
11	16	18.7294759	-2.73	2.73	7.5	17.06%
12	25	18.4565283	6.54	6.54	42.8	26.17%
13		19.1108755

	α=	0.2		Exponential smoothing
period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error	Abs %error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²	| et/Dt |
1	17
2	21	17	4.00	4.00	16.0	19.05%
3	16	17.8	-1.80	1.80	3.2	11.25%
4	24	17.44	6.56	6.56	43.0	27.33%
5	17	18.752	-1.75	1.75	3.1	10.31%
6	18	18.4016	-0.40	0.40	0.2	2.23%
7	22	18.32128	3.68	3.68	13.5	16.72%
8	20	19.057024	0.94	0.94	0.9	4.71%
9	21	19.2456192	1.75	1.75	3.1	8.35%
10	19	19.5964954	-0.60	0.60	0.4	3.14%
11	16	19.4771963	-3.48	3.48	12.1	21.73%
12	25	18.781757	6.22	6.22	38.7	24.87%
13		20.0254056

forecast for week 13, when α=0.1 = 19.1108755

forecast for week 13, when α=0.2 = 20.0254056

--------------------

b)

      

An α = 0.2 smoothing constant provides the more accurate forecast, with an overall MSE of 12.19

c)

An α = 0.2 smoothing constant provides the more accurate forecast, with an overall MAE of 2.83

      

d)

An α = 0.1 smoothing constant provides the more accurate forecast, with an overall MAPE of 13.34%