Question

Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits.

Week	Sales (1,000s of gallons)
1	16
2	22
3	17
4	23
5	15
6	17
7	21
8	19
9	20
10	18
11	15
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

for α =0.1

period	value	forecast	error	error^2	|A-F|/A
1	16
2	22	16.00	6.000	36.000	0.2727
3	17	16.60	0.400	0.160	0.0235
4	23	16.64	6.360	40.450	0.2765
5	15	17.28	2.276	5.180	0.1517
6	17	17.05	0.048	0.002	0.0028
7	21	17.04	3.956	15.653	0.1884
8	19	17.44	1.561	2.436	0.0821
9	20	17.60	2.405	5.783	0.1202
10	18	17.84	0.164	0.027	0.0091
11	15	17.85	2.852	8.135	0.1901
12	23	17.57	5.433	29.518	0.2362
13		18.11
		average	2.86	13.031	14.12%
			MAE	MSE	MAPE

for α =0.2

period	value	forecast	error	error^2	|A-F|/A
1	16
2	22	16.00	6.000	36.000	0.2727
3	17	17.20	0.200	0.040	0.0118
4	23	17.16	5.840	34.106	0.2539
5	15	18.33	3.328	11.076	0.2219
6	17	17.66	0.662	0.439	0.0390
7	21	17.53	3.470	12.041	0.1652
8	19	18.22	0.776	0.602	0.0408
9	20	18.38	1.621	2.627	0.0810
10	18	18.70	0.703	0.495	0.0391
11	15	18.56	3.563	12.693	0.2375
12	23	17.85	5.150	26.521	0.2239
13		18.88
		average	2.85	12.422	14.43%
			MAE	MSE	MAPE

from above:

a)

week	alpha=0.1	alpha=0.2
13th week	18.11	18.88

b)

an α =0.2 ,,,,,,,with an overall MSE of 12.42

c)

an α =0.2 ,,,,,,,with an overall MAE of 2.85

d)

an α =0.1 ,,,,,,,with an overall MAE of 14.12 %