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.
Phillips, Peter C.B. and Magdalinos, Tassos, "Inconsistent VAR Regression with Common Explosive Roots" (2011). Cowles Foundation Discussion Papers. 2118.