Limit Theory for VARs with Mixed Roots Near Unity

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.