Further curiosa in 'spurious' cointegration. Southampton, UK, University of Southampton
(Discussion Papers in Economics and Econometrics 9704).
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O'Brien (1996) examined the effect of intercept shifts in I(1) processes upon Johansen's cointegration tests. In the case where the statistical model used for testing fails to take into account one or more intercept shifts, it was shown that unrelated random walks will appear cointegrated with probability 1 as the sample size tends to infinity.
This paper generalises these results, then extends the investigation to include the effects of prior unit root tests, and of testing for zeros in the cointegrating vectors, to reveal the problem. Monte Carlo experiments suggest the effect remains noticeable in samples of moderate size. An asymptotic analysis of the Engle-Granger procedure for testing for cointegration explains other published results which indicate that this procedure has rather different difficulties when faced with intercept shifts.
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