Order determination in general vector autoregressions

TL;DR

This paper demonstrates that common methods for determining the order of vector autoregressions are valid regardless of stationarity assumptions and can handle deterministic terms, extending their applicability.

Contribution

It shows that likelihood ratio tests and information criteria can be used for order determination in VARs without stationarity restrictions, supported by new proofs.

Findings

Methods are valid regardless of characteristic roots.

Applicable in presence of deterministic terms.

Extends existing theory to non-stationary VARs.

Abstract

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.