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	23
3	14
4	25
5	17
6	16
7	22
8	19
9	21
10	19
11	17
12	23

(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

for exponential smoothing: next period forecast =α*last period actual+(1-α)*last period forecast

at alpha =0.1:

week	value	forecast	error	error^2	|A-F|/A
1	17
2	23	17.00	6.000	36.000	0.260869565
3	14	17.60	3.600	12.960	0.257142857
4	25	17.24	7.760	60.218	0.3104
5	17	18.02	1.016	1.032	0.059764706
6	16	17.91	1.914	3.665	0.11965
7	22	17.72	4.277	18.293	0.194410909
8	19	18.15	0.849	0.721	0.044701895
9	21	18.24	2.764	7.642	0.13163821
10	19	18.51	0.488	0.238	0.025682219
11	17	18.56	1.561	2.436	0.091813768
12	23	18.40	4.595	21.116	0.19979345
13		18.86	34.825	164.322	1.696
		average	3.17	14.938	15.42%
			MAE	MSE	MAPE

at alpha=0.2

week	value	forecast	error	error^2	|A-F|/A
1	17
2	23	17.00	6.000	36.000	0.260869565
3	14	18.20	4.200	17.640	0.3
4	25	17.36	7.640	58.370	0.3056
5	17	18.89	1.888	3.565	0.111058824
6	16	18.51	2.510	6.302	0.1569
7	22	18.01	3.992	15.934	0.18144
8	19	18.81	0.193	0.037	0.010176
9	21	18.85	2.155	4.643	0.102603581
10	19	19.28	0.276	0.076	0.014539992
11	17	19.22	2.221	4.933	0.130647522
12	23	18.78	4.223	17.835	0.183617117
13		19.62	35.299	165.334	1.757
		average	3.21	15.030	15.98%
			MAE	MSE	MAPE

a)

week	alpha =0.1		alpha =0.2
13	18.86		19.62

b)

0.1 smoothing constant provides the more accurate forecast, with an overall MSE of 14.94

c)

0.1 smoothing constant provides the more accurate forecast, with an overall MAE of 3.17

d)

0.1 smoothing constant provides the more accurate forecast, with an overall MAPE of 15.42 %