Hi Roberto,
The error message “the non-seasonal autoregressive polynomial is unstable” indicates that some of the eigenvalues of the AR part of the series are outside the unit circle, hence non-stationarity. Similarly, the error “the non-seasonal moving average polynomial is non-invertible” shows explosion of the MA roots, hence non-invertibility.
Practically it is not a good idea to fit a high-order ARMA model. It might require a huge sample size to provide a good estimate on a ARMA(3,3) model, even if the data are simulated from the true model. To avoid those error messages, be parsimonious in model specification, say ARMA(1,1). If you really want a high-order model, you may consider informative priors to shrink the coefficients.
Thank you.
Regards,
Hang Qian
