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	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22

(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)

For alpha = 0.1

period	demand	Forecast ŷt+1 = yt*α + ŷt*(1-α)	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	17.000	4.00	4.00	16.00	19.05%
3	19	17.400	1.60	1.60	2.56	8.42%
4	23	17.560	5.44	5.44	29.59	23.65%
5	18	18.104	-0.10	0.10	0.01	0.58%
6	16	18.094	-2.09	2.09	4.38	13.09%
7	20	17.884	2.12	2.12	4.48	10.58%
8	18	18.096	-0.10	0.10	0.01	0.53%
9	22	18.086	3.91	3.91	15.32	17.79%
10	20	18.478	1.52	1.52	2.32	7.61%
11	15	18.630	-3.63	3.63	13.18	24.20%
12	22	18.267	3.73	3.73	13.94	16.97%
		18.640

For alpha = 0.2

period	demand	Forecast ŷt+1 = yt*α Forecast ŷt+1 = yt*α + ŷt*(1-α) + ŷt*(1-α)	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	17.000	4.00	4.00	16.00	19.05%
3	19	17.800	1.20	1.20	1.44	6.32%
4	23	18.040	4.96	4.96	24.60	21.57%
5	18	19.032	-1.03	1.03	1.07	5.73%
6	16	18.826	-2.83	2.83	7.98	17.66%
7	20	18.260	1.74	1.74	3.03	8.70%
8	18	18.608	-0.61	0.61	0.37	3.38%
9	22	18.487	3.51	3.51	12.34	15.97%
10	20	19.189	0.81	0.81	0.66	4.05%
11	15	19.351	-4.35	4.35	18.94	29.01%
12	22	18.481	3.52	3.52	12.38	15.99%
		19.185

b)

For alpha = 0.1

MSE=   Σ(et)²/n =    9.25

For alpha = 0.2

MSE=   Σ(et)²/n =    8.98

Since MSE for For alpha = 0.2 is lesser than For alpha = 0.1 we will select alpha = 0.2

c)

For alpha = 0.1

MAE=   Σ |et|/n =    2.57

For alpha = 0.2

MAE=   Σ |et|/n =    2.60

Since MSE for For alpha = 0.1 is lesser than For alpha = 0.2 we will select alpha = 0.1

d)

For alpha = 0.1

MAPE=   Σ | et/Dt |/n =    12.95%

For alpha = 0.2

MAPE=   Σ | et/Dt |/n =    13.40%

Since MAPE for For alpha = 0.1 is lesser than For alpha = 0.2 we will select alpha = 0.1

Please revert back in case of any doubt.

Please upvote. Thanks in advance.