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 | .

• 3.48
• 4.31
• 5.54
• 6.47
• 7.63

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.