SOA Exam SRM Sample Question 3

Study guide: Exam SRM

You are given:

i) The random walk model

$y_t = y_0 + c_1 + c_2 + \cdots + c_t$

where $c_t,\ t = 0, 1, 2, \ldots, T$ denote observations from a white noise process.

ii) The following nine observed values of $c_t$ :

$t$	11	12	13	14	15	16	17	18	19
$c_t$	2	3	5	3	4	2	4	1	2

iii) The average value of $c_1, c_2, \ldots, c_{10}$ is 2.

iv) The 9 step ahead forecast of $y_{19}$ , $\hat{y}_{19}$ , is estimated based on the observed value of $y_{10}$ .

Calculate the forecast error, $y_{19} - \hat{y}_{19}$ .

Concepts tested