Inconsistent VAR Regression With Common Explosive Roots
Nielsen (2009) shows that vector autoregression is inconsistent when there are common explosive roots with geometric multiplicity greater than unity. This paper discusses that result, provides a co-explosive system extension and an illustrative example that helps to explain the finding, gives a consistent instrumental variable procedure, and reports some simulations. Some exact limit distribution theory is derived and a useful new reverse martingale central limit theorem is proved. Financial exuberance and market bubbles have led to a new interest among empirical researchers in autoregressive time series with explosive roots.