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A RESIDUAL-BASED LM-TYPE TEST AGAINST FRACTIONAL COINTEGRATION

Published online by Cambridge University Press:  03 November 2006

Uwe Hassler  and
Jörg Breitung
Uwe Hassler
Affiliation:
Goethe-University Frankfurt
Jörg Breitung
Affiliation:
University of Bonn
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Abstract

Nonstationary integrated time series may be fractionally cointegrated. Here we propose a test for the null hypothesis of no cointegration. It builds on the asymptotically normal Lagrange multiplier (LM) test against fractional alternatives applied to single equation residuals. It is shown that the LM test applied naively to residuals from a static level regression does not retain asymptotic normality. However, when the LM statistic is employed with residuals from a regression of differenced variables, then the test statistic is shown to have a standard normal limiting distribution. Monte Carlo experiments establish its relevance in finite samples.We thank Norbert Christopeit and three anonymous referees for corrections and very valuable comments.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 6 , December 2006 , pp. 1091 - 1111
Copyright
© 2006 Cambridge University Press

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