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A time series was observed at times 0, 1, …, 100. The last four observations along with estimates based on exponential and double exponential smoothing with [math]w = 0.8[/math] are:
| Time (t) | 97 | 98 | 99 | 100 |
|---|---|---|---|---|
| Observation ( [math]y_t[/math] ) | 96.9 | 98.1 | 99.0 | 100.2 |
| Estimates ( [math]\hat{s_1}(t) [/math] | 93.1 | 94.1 | 95.1 | |
| Estimates ( [math]\hat{s_2}(t)[/math] | 88.9 | 89.9 |
All forecasts should be rounded to one decimal place and the trend should be rounded to three decimal places.
Let [math]F[/math] be the predicted value of [math]y_{102}[/math] using exponential smoothing with [math]w = 0.8.[/math]
Let [math]G[/math] be the predicted value of [math]y_{102}[/math] using double exponential smoothing with [math]w = 0.8.[/math]
Calculate the absolute difference between [math]F[/math] and [math]G[/math], [math]| F − G |[/math] .
- 0.0
- 2.1
- 4.2
- 6.3
- 8.4
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
- Created by Admin, May 25'23