You are given the following eight observations from a time series that follows a random walk model:
| Time (t) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Observation ( [math]y_t[/math] ) | 3 | 5 | 7 | 8 | 12 | 15 | 21 | 22 |
You plan to fit this model to the first five observations and then evaluate it against the last three observations using one-step forecast residuals. The estimated mean of the white noise process is 2.25.
Let F be the mean error (ME) of the three predicted observations.
Let G be the mean square error (MSE) of the three predicted observations.
Calculate the absolute difference between F and G, | F − G | .
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Key: B
The three one-step predicted values are 12+2.25 = 14.25; 15+2.25 = 17.25; and 21+2.25 = 23.25.
The errors are 15 – 14.25 = 0.75; 21 – 17.25 = 3.75; and 22 – 23.25 = –1.25.
F = (0.75 + 3.75 – 1.25)/3 = 1.083
G = (0.752 + 3.752 + 1.252)/3 = 5.396
The absolute difference is 4.313.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.