问一道题：NO.PZ2016062402000045

问题如下：

Suppose $\sigma_t^2$ is the estimated variance at time t and $\mu_t$ is the realized return at t. Which of the following GARCH(1,1) models will take the longest time to revert to its mean?

选项：

$\sigma_t^2=0.04+0.02\mu_{t-1}^2+0.92\sigma_{t-1}^2$

$\sigma_t^2=0.02+0.04\mu_{t-1}^2+0.94\sigma_{t-1}^2$

$\sigma_t^2=0.03+0.02\mu_{t-1}^2+0.95\sigma_{t-1}^2$

$\sigma_t^2=0.03+0.03\mu_{t-1}^2+0.93\sigma_{t-1}^2$

解释：

The persistence $(\alpha_1+\beta)$span> is，respectively，0.94, 0.98, 0.97, and 0.96. Hence the model with the highest persistence will take the longest time to revert to the mean.