Question

The following data is the unemployment rate in a metropolitan community over the last 10 years. Use exponential smoothing with a smoothing constant of a = 0.2, 0.4, 0.6, and 0.8 to find the best forecast for unemployment for next year. Using mean absolute deviation which forecast constant provides the best prediction of unemployment? Why?

Year	Rate	Year	Rate
1	7.2	6	5.5
2	7.0	7	6.7
3	6.2	8	7.4
4	5.0	9	6.8
5	5.3	10	6.1

Answer 1

Exponential smoothing method formula for forecasting is

    where s_t is forecasted value for t period, x_t is actual value for t period

smoothing factor		0.2	0.4	0.6	0.8		0.2		0.4		0.6		0.8
Year	Rate	Forecast	Forecast	Forecast	Forecast	Difference	Abs.Diff.	Difference	Abs.Diff.	Difference	Abs.Diff.	Difference	Abs.Diff.
1	7.2	7.2	7.2	7.2	7.2	0.0
2	7	7.2	7.1	7.1	7.0	0.2	0.2	0.1	0.1	0.1	0.1	0.0	0.0
3	6.2	7.0	6.8	6.6	6.4	0.8	0.8	0.6	0.6	0.4	0.4	0.2	0.2
4	5.5	6.7	6.3	5.9	5.7	1.2	1.2	0.8	0.8	0.4	0.4	0.2	0.2
5	5.3	6.4	5.9	5.5	5.4	1.1	1.1	0.6	0.6	0.2	0.2	0.1	0.1
6	5.5	6.2	5.7	5.5	5.5	0.7	0.7	0.2	0.2	0.0	0.0	0.0	0.0
7	6.7	6.3	6.1	6.2	6.5	-0.4	0.4	-0.6	0.6	-0.5	0.5	-0.2	0.2
8	7.4	6.5	6.6	6.9	7.2	-0.9	0.9	-0.8	0.8	-0.5	0.5	-0.2	0.2
9	6.8	6.6	6.7	6.9	6.9	-0.2	0.2	-0.1	0.1	0.1	0.1	0.1	0.1
10	6.1	6.5	6.5	6.4	6.3	0.4	0.4	0.4	0.4	0.3	0.3	0.2	0.2
						Total	5.8		4.0		2.4		1.2
						MAD	0.6		0.4		0.3		0.1

Lowest MAD is for 0.8 smoothing constant