In practice, how to evaluate whether a AR(P) process is stationary or not?
How to determine the order for the AR and MA model?
Extract the roots of the polynomial. If all the roots are outside the unit circle then the process is stationary. Model identification aids can be found on the web. Fundamentally the pattern of the ACF’s and the pattern of the PACF’s are used to identify which model might be a good starting model. If there are more significant ACF’s than significant PACF’s then an AR model is suggested as the ACF is dominant. if the converse is true where the PACF is dominant then an MA model might be appropriate. The order of the model is suggested by the number of significant values in the subordinate.