  In the application of autoregressive models the order of the model is often
estimated using either a sequence of likelihood ratio tests, a likelihood based
information criterion, or a residual based test. The properties of such
procedures has been discussed extensively under the assumption that the
characteristic roots of the autoregression are stationary. While non-stationary
situations have also been considered the results in the literature depend on
conditions to the characteristic roots. It is here shown that these methods for
lag length determination can be used regardless of the assumption to the
characteristic roots and also in the presence of deterministic terms. The
proofs are based on methods developed by C. Z. Wei in his joint work with T. L.
Lai.
