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A RESIDUAL-BASED TEST FOR STOCHASTIC COINTEGRATION

Published online by Cambridge University Press:  15 March 2006

Brendan McCabe ,
Stephen Leybourne  and
David Harris
Brendan McCabe
Affiliation:
University of Liverpool
Stephen Leybourne
Affiliation:
University of Nottingham
David Harris
Affiliation:
University of Melbourne
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Abstract

We consider the problem of hypothesis testing in a modified version of the stochastic integration and cointegration framework of Harris, McCabe, and Leybourne (2002, Journal of Econometrics 111, 363–384). This nonlinear setup allows for volatility in excess of that catered for by the standard integration/cointegration paradigm through the introduction of nonstationary heteroskedasticity. We propose a test for stochastic cointegration against the alternative of no cointegration and a secondary test for stationary cointegration against the heteroskedastic alternative. Asymptotic distributions of these tests under their respective null hypotheses are derived, and consistency under their respective alternatives is established. Monte Carlo evidence suggests that the tests will perform well in practice. An empirical application to the term structure of interest rates is also given.We are most grateful to the Associate Editor and two anonymous referees for providing helpful comments on earlier versions of this paper.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 3 , June 2006 , pp. 429 - 456
Copyright
© 2006 Cambridge University Press

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