# Does dynare allow for heteroskedastic variance in shocks

Dear All,
I am recently doing a project on DSGE model with heteroskedastic variance in structural shocks, I am wondering that does Dynare allow structural shocks to be specified with heteroskedastic variances?
Thank you!
Best wishes,
Jesse

What exactly do you have in mind? What is the form of heteroskedasticity? Stochastic volatility? GARCH?

Dear Johannes,
I mean GARCH. When specifying the variance of a structural shock, can I use a latent endogenous variable instead of a parameter? the latent endogenous variable represents the time varying variance.
Look forward to hearing from you.
Best,
Jesse

In the shocks-block you can always only define homoskedastic shocks. But this is not really limiting. You can write any heteroskedastic shock process as the product of a process defining the time-varying standard deviation times the homoskedastic shock:

An example is the stochastic volatility process from github.com/JohannesPfeifer/DSGE_mod/blob/master/Born_Pfeifer_2014/Born_Pfeifer_RM_Comment.mod

[code]model;
eps_r=rho_eps_r*eps_r(-1)+exp(sigma_r)u_r;
sigma_r=(1-rho_sigma_r)sigma_r_bar+rho_sigma_rsigma_r(-1)+eta_r
u_sigma_r;
end;

shocks;
var u_r; stderr 1;
var u_sigma_r; stderr 1;
end;
[/code]
All exogenous shocks here are homeskedastic, but simga_r makes the shock entering the eps_r equation heteroskedastic.

Dear Johannes,
Thank you very much.
In fact, I have tried this form already, I have a question for eps_r=rho_eps_r*eps_r(-1)+exp(sigma_r)*u_r;
after log-linearisation of this equation in Dynare, log of shock u_r no longer follows normal distribution, can I still apply Kalman filter in estimation? because Kalman filter requires all exogenous shocks to be normal.
Thank you again and look forward to hearing from you.
Best wishes,
Jesse

Of course not. The Kalman filter works for linear Gaussian state space models. Heteroskedastic models are not linear anymore. You can simulate them in Dynare, but you cannot estimate them yet. The particle filter only works up to order=2, not 3