Hello I would like to know how would you discretize the AR(1) process of technology in a standart RBC model when there is stochastic productivity's standard deviation. Namely I have:

Technology $Z_t$ follows a log-normal AR(1) process with stochastic volatility $\sigma_{t}^{Z}$ : $$ \begin{aligned} \log Z_{t} &=\rho^{Z} \log Z_{t-1}+\sigma_{t}^{Z} \varepsilon_{t}^{Z} \\ \varepsilon_{t}^{Z} & \sim \mathcal{N}(0,1) \end{aligned} $$ with stochastic volatility $\sigma_{t}^{Z}$ also following a log-normal process $$ \begin{aligned} \log \sigma_{t}^{Z} &=\left(1-\rho^{S V}\right) \log \bar{\sigma}+\rho^{S V} \log \sigma_{t-1}^{Z}+\varepsilon_{t}^{S V} \\ \varepsilon_{t}^{S V} & \sim \mathcal{N}\left(0, \sigma^{S V}\right) \end{aligned} $$

To discretize $Z_t$ I usually use the Tauchen-Hussey procedure, but since $\sigma_{t}^{Z}$ is now stochastic I don't know how to do it anymore.

Thank you


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