Hi, I’m trying to use the Chebyshev polynomial method to solve a RBC model.

I know in Dynare where the perturbation method is used, the model needs to be stationary so that the policy functions are approximated around the steady state.

However, for Chebyshev projection, only a projection range of state variables are needed. As a result, if I assume there is a stochastic trend in technology, can I solve the nonstationary model with projection method directly (there is an optimal solution), or do I still need to first rescale the model, and then solve the stationary model?

My understanding is that, the projection method is purely makes the residuals as close to zero as possible. So even if the model is nonstationary, the approximated policy function should still be correct. But I’m not sure because naturally we detrend the model.