Limit Theory for VARs with Mixed Roots Near Unity

Abstract

Limit theory is developed for nonstationary vector autoregression (VAR) with mixed roots in the vicinity of unity involving persistent and explosive components. Statistical tests for common roots are examined and model selection approaches for discriminating roots are explored. The results are useful in empirical testing for multiple manifestations of nonstationarity – in particular for distinguishing mildly explosive roots from roots that are local to unity and for testing commonality in persistence.

Keywords:

• Common roots
• Local to unity
• Mildly explosive
• Mixed roots
• Model selection
• Persistence
• Tests of common roots

JEL Classification:

• C22

ACKNOWLEDGMENTS

This paper is based on the first part of a Yale take home examination by the first author in 2010/2011. The authors thank the Editor and two referees for helpful and constructive comments on the original version.

Notes

¹For example, asymptotic critical values might be computed for the limit distribution (2.13) with Σ =I and .