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Dear All,
I have a very basic question, does all observed variables entering DSGE model should just be mean stationary or must be both mean and co-variance stationary?
I mean can a variable that is mean stationary but heteroskedastic entering the DSGE model as observed variable?
Thank you very much and look forward to hearing from you.
Best,
Jesse

Your terminology is not precise. There are forms of heteroskedasticity that are consistent with covariance stationarity.

What you definitely need is for your variance to exist, i.e. be finite. You can have heteroskedastic data for estimation, but at

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order=1

your model will not be able to capture this, as it will work with a linear model and a therefore constant second moment.

Dear Johannes,
Thank you very much for your helpful comments.
Do you mean order=1 (linear DSGE model)can Not include observed variables with time varying variances,
but order=2(nonlinear DSGE model) can include observed variables with time varying variances?
Thank you very much and look forward to hearing from you.
Jesse

In a linear DSGE model, you can include variables with time-varying variances, but the model will not pick up this heteroskedaticity. The model will simply aim at getting the average variance right. In a non-linear model, the model-implied observed variables can be heteroskedastic even if the fundamental shocks driving the model being homoskedastic.