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

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

a)

for alpha =0.1:

week	value	forecast	error	error^2	|A-F|/A
1	17
2	21	17.00	4.000	16.000	0.19047619
3	16	17.40	1.400	1.960	0.0875
4	24	17.26	6.740	45.428	0.280833333
5	17	17.93	0.934	0.872	0.054941176
6	18	17.84	0.159	0.025	0.008855556
7	22	17.86	4.143	17.168	0.188339091
8	20	18.27	1.729	2.990	0.0864557
9	21	18.44	2.556	6.534	0.121723933
10	19	18.70	0.301	0.090	0.015820123
11	16	18.73	2.729	7.450	0.170592243
12	25	18.46	6.543	42.817	0.261738868
13		19.11	31.236	141.335	1.467
		average	2.840	12.849	13.34%
			MAE	MSE	MAPE

fro alpha =0.2:

week	value	forecast	error	error^2	|A-F|/A
1	17
2	21	17.00	4.000	16.000	0.19047619
3	16	17.80	1.800	3.240	0.1125
4	24	17.44	6.560	43.034	0.273333333
5	17	18.75	1.752	3.070	0.103058824
6	18	18.40	0.402	0.161	0.022311111
7	22	18.32	3.679	13.533	0.167214545
8	20	19.06	0.943	0.889	0.0471488
9	21	19.25	1.754	3.078	0.083541943
10	19	19.60	0.596	0.356	0.031394493
11	16	19.48	3.477	12.091	0.217324768
12	25	18.78	6.218	38.667	0.248729719
13		20.03	31.182	134.118	1.497
		average	2.835	12.193	13.61%
			MAE	MSE	MAPE

a)

week	alpha =0.1		alpha =0.2
13	19.11		20.03

b)

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

c) alpha =0.2  smoothing constant provides the more accurate forecast, with an overall MAE=2.783

d)

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