10. Suppose X follows an AR(1) model: X(t) = 0.1 + 0.8*X(t-1) + e(t), where, E(e(t)) = 0. What is the long term mean of X?

A. 0.1250

B. 0.5000

C. 2.0000

D. 0.0000

Correct answer is B

A is incorrect. This solution incorrectly calculates the long term mean of X to be 0.1/0.8 = 0.125

B is correct. For a AR(1) model of the form: X(t) = alpha + beta X(t-1) + e(t), where E[e(t)] = 0, the long term mean of X is alpha / (1-beta).

For this problem, the long term mean of X is 0.5000 = 0.1 / (1.0 - 0.8).

C is incorrect. This solution incorrectly calculates the long term mean of X to be (1.0 - 0.8) / 0.1 = 2.000

D is incorrect. 

Reference:  Philippe Jorion, Value At Risk, 3rd ed. Chapter 9.

Type of Question: Quantitative Analysis

非常感谢