It would be great if you help me with this, as I’ve been stuck on this problem now for quite some time. Many thanks in advance for your help!

As you can see from the attached pdf below, two of my parameters, ZRHO_AJ (persistence parameter) and THETAS, are very close to their boundaries. In fact ZRHO_AJ hits it, the other parameters look fine. I should mention that both parameters follow a beta distribution and I’m estimating in total 36 parameters.

My data has been either quadratically detrended or in one case just demeaned, as it is a vacancy rate. For the mode finding I use the following options:

Usually when this happens the model wants to tell you something. You can clearly see that the data wants to have a unit root in one variable. Most of the time this is a sign of a wrong observation equation where the model can only reconcile the data with the model by having a unit root, i.e. permanent shocks that move the mean.

Thanks a lot for your help. Would you recommend to write the observeration equation, which causes the “trouble”, in first differences rather than in deviation from the steady state? At the moment my observation equations are entered in a nonlinear form e.g.

Observeration equation in model: HR_obs = HR/HR_SS - 1

Data: ln(HR_data) - ln(HR_data_mean)

Which would then become:

New observeration equation in model: HR_obs = HR/HR(-1) - 1

Sorry I forgot to mention that. Here in this specific case the underlying data corresponds to the rental vacancy rate. Due to data unavailability, I use it as a proxy for the rental housing stock in my model, in order to pick up the dynamics of the rental housing market. However, a unit root test showed that the data is nonstationary and judging from the graph (see below) suggests that there is a slight upward trend for the given sample period. Would you recommend to detrend it or using first differences?