13.53 It’s exponential.
Exponential smoothing models are so named because the weights
decrease in value exponentially. For this exercise, take . Use software to do the calculations.
13.53
(a)–(c)
0.1 | 0.5 | 0.9 | |
---|---|---|---|
1 | 0.1000 | 0.5000 | 0.9000 |
2 | 0.0900 | 0.2500 | 0.0900 |
3 | 0.0810 | 0.1250 | 0.0090 |
4 | 0.0729 | 0.0625 | 0.0009 |
5 | 0.0656 | 0.0313 | 9.E-05 |
6 | 0.0590 | 0.0156 | 9.E-06 |
7 | 0.0531 | 0.0078 | 9.E-07 |
8 | 0.0478 | 0.0039 | 9.E-08 |
9 | 0.0430 | 0.0020 | 9.E-09 |
10 | 0.0387 | 0.0010 | 9.E-10 |
(e) The higher values put more weight on the current observation, so the curve with . (f) 0.3487, 0.000977, 1E-10. puts the most weight on .