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COINTEGRATION RANK TESTING UNDER CONDITIONAL 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 conventional Gaussian-based cointegrating rank tests of Johansen (1996, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models) in the case where the vector of series under test is driven by globally stationary, conditionally heteroskedastic (martingale difference) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either independent and identically distributed (i.i.d.) or (strict and covariance) stationary martingale difference innovations. We then propose wild bootstrap implementations of the cointegrating rank tests and demonstrate that the associated bootstrap rank statistics replicate the first-order asymptotic null distributions of the rank statistics. We show that the same is also true of the corresponding rank tests based on the i.i.d. bootstrap of Swensen (2006, Econometrica 74, 1699–1714). The wild bootstrap, however, has the important property that, unlike the i.i.d. bootstrap, it preserves in the resampled data the pattern of heteroskedasticity present in the original shocks. Consistent with this, numerical evidence suggests that, relative to tests based on the asymptotic critical values or the i.i.d. bootstrap, the wild bootstrap rank tests perform very well in small samples under a variety of conditionally heteroskedastic innovation processes. An empirical application to the term structure of interest rates is given.

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 Cavaliere and Taylor both visited CREATES, whose hospitality is gratefully acknowledged. We are grateful to three anonymous referees and to Peter Phillips, Søren Johansen, Anders Swensen, and Carsten Trenkler for their helpful and constructive comments on earlier versions of this paper. We also thank Steve Leybourne for providing us with the data used in Section 6. Cavaliere and Rahbek thank the Danish Social Sciences Research Council, project 2114-04-001, for continuing financial support. Cavaliere also acknowledges financial support from MIUR PRIN 2007 grants. Rahbek is also affiliated with CREATES, funded by the Danish National Research Foundation.

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