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

(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

for alpha =0.1:

week	value	forecast	error	error^2	|A-F|/A
1	17
2	21	17.000	4.000	16.000	0.1905
3	16	17.400	1.400	1.960	0.0875
4	24	17.260	6.740	45.428	0.2808
5	17	17.934	0.934	0.872	0.0549
6	18	17.841	0.159	0.025	0.0089
7	22	17.857	4.143	17.168	0.1883
8	20	18.271	1.729	2.990	0.0865
9	21	18.444	2.556	6.534	0.1217
10	19	18.699	0.301	0.090	0.0158
11	16	18.729	2.729	7.450	0.1706
12	25	18.457	6.543	42.817	0.2617
		total	31.236	141.335	1.467
		average	2.840	12.85	13.339%
			MAE	MSE	MAPE

for alpha =0.2

week	value	forecast	error	error^2	|A-F|/A
1	17
2	21	17.000	4.000	16.000	0.1905
3	16	17.800	1.800	3.240	0.1125
4	24	17.440	6.560	43.034	0.2733
5	17	18.752	1.752	3.070	0.1031
6	18	18.402	0.402	0.161	0.0223
7	22	18.321	3.679	13.533	0.1672
8	20	19.057	0.943	0.889	0.0471
9	21	19.246	1.754	3.078	0.0835
10	19	19.596	0.596	0.356	0.0314
11	16	19.477	3.477	12.091	0.2173
12	25	18.782	6.218	38.667	0.2487
		total	31.182	134.118	1.497
		average	2.835	12.19	13.609%
			MAE	MSE	MAPE

b)

alpha =0.2 is better since for it MSE is smaller

with an overall MSE of 12.193~ 12.19

c)

alpha =0.2 is better since for it MAE is smaller

with an overall MAE of =2.835~ 2.83

D)

alpha =0.1 is better since for it MAE is smaller

with an overall MAPE of =13.339 %