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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.
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