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COINTEGRATION RANK TESTING UNDERCONDITIONAL HETEROSKEDASTICITY

Published online by Cambridge University Press:  22 March 2010

Giuseppe Cavaliere ,
Anders Rahbek  and
A.M. Robert Taylor
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Abstract

We analyze the properties of the conventionalGaussian-based cointegrating rank tests of Johansen(1996, Likelihood-Based Inference in CointegratedVector Autoregressive Models) in the case where thevector of series under test is driven by globallystationary, conditionally heteroskedastic(martingale difference) innovations. We firstdemonstrate that the limiting null distributions ofthe rank statistics coincide with those derived byprevious authors who assume either independent andidentically distributed (i.i.d.) or (strict andcovariance) stationary martingale differenceinnovations. We then propose wild bootstrapimplementations of the cointegrating rank tests anddemonstrate that the associated bootstrap rankstatistics replicate the first-order asymptotic nulldistributions of the rank statistics. We show thatthe same is also true of the corresponding ranktests based on the i.i.d. bootstrap of Swensen(2006, Econometrica 74, 1699–1714).The wild bootstrap, however, has the importantproperty that, unlike the i.i.d. bootstrap, itpreserves in the resampled data the pattern ofheteroskedasticity present in the original shocks.Consistent with this, numerical evidence suggeststhat, relative to tests based on the asymptoticcritical values or the i.i.d. bootstrap, the wildbootstrap rank tests perform very well in smallsamples under a variety of conditionallyheteroskedastic innovation processes. An empiricalapplication to the term structure of interest ratesis given.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1719 - 1760
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

Parts of this paper were written while Cavaliereand Taylor both visited CREATES, whose hospitalityis gratefully acknowledged. We are grateful tothree anonymous referees and to Peter Phillips,Søren Johansen, Anders Swensen, and CarstenTrenkler for their helpful and constructivecomments on earlier versions of this paper. Wealso thank Steve Leybourne for providing us withthe data used in Section 6. Cavaliere and Rahbekthank the Danish Social Sciences Research Council,project 2114-04-001, for continuing financialsupport. Cavaliere also acknowledges financialsupport from MIUR PRIN 2007 grants. Rahbek is alsoaffiliated with CREATES, funded by the DanishNational Research Foundation.

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