SOA Exam SRM Sample Question 21

Study guide: Exam SRM

A random walk is expressed as

$y_t = y_{t-1} + c_t \quad \text{for } t = 1, 2, \ldots$

where

$E(c_t) = \mu_c \text{ and } Var(c_t) = \sigma_c^2, \quad t = 1, 2, \ldots$

Determine which statements is/are true with respect to a random walk model.

I. If $\mu_c \neq 0$ , then the random walk is nonstationary in the mean.
II. If $\sigma_c^2 = 0$ , then the random walk is nonstationary in the variance.
III. If $\sigma_c^2 > 0$ , then the random walk is nonstationary in the variance.
A) None
B) I and II only
C) I and III only
D) II and III only
E) The correct answer is not given by (A), (B), (C), or (D).

Concepts tested