will state space model be affected by Gaussian mixture shock

[Jesse]

Dear All,
I just have a question. If one of my structural shocks follows a Gaussian mixture process, and I included it into my DSGE model, will my DSGE model can still be transformed into a state space model after log linearization?
Thank you and any ideas will be helpful!
Jesse

[jpfeifer]

Due to the way first order perturbation works, your shock will always be approximated via its mean and variance, effectively being rendered a normal distribution.