I have some shocks in my log-linearized model which follow an AR(1) process, like this
\log a_{t} = (1 - \rho_{a})\log a + \rho_{a} \log a_{t-1} +\sigma_{a}\epsilon_{a}
in Dynare, I code them like this:
ahat = rho_a*ahat(-1)+ea
Now, I want to introduce an uncertainty shock in this model, like this
\log a_{t} = (1 - \rho_{a})\log a + \rho_{a} \log a_{t-1} +\sigma_{t-1}^{a}\epsilon_{a}
where \sigma_{t-1}^{a} follows
\log \sigma_{t} = (1 - \rho_{\sigma})\log \sigma + \rho_{\sigma} \log \sigma_{t-1} +\sigma_{t-1}^{\sigma}\epsilon_{\sigma}
I wonder how I should log-linearize this. I want to log-linearize this myself since I already have rest of the model log-linearized.