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TESTS FOR NONLINEARCOINTEGRATION

Published online by Cambridge University Press:  07 October 2009

In Choi  and
Pentti Saikkonen
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Abstract

This paper develops tests for the null hypothesis ofcointegration in the nonlinear regression model withI(1) variables. The teststatistics we use in this paper are Kwiatkowski,Phillips, Schmidt, and Shin’s (1992; KPSS hereafter)tests for the null of stationarity, though usingother kinds of tests is also possible. The tests areshown to depend on the limiting distributions of theestimators and parameters of the nonlinear modelwhen they use full-sample residuals from thenonlinear least squares and nonlinear leads-and-lagsregressions. This feature makes it difficult to usethem in practice. As a remedy, this paper developstests using subsamples of the regression residuals.For these tests, first, the nonlinear least squaresand nonlinear leads-and-lags regressions are run andresiduals are calculated. Second, the KPSS tests areapplied using subresiduals of sizeb. As long asb/T → 0 asT → ∞, where Tis the sample size, the tests using the subresidualshave limiting distributions that are not affected bythe limiting distributions of the full-sampleestimators and the parameters of the model. Third,the Bonferroni procedure is used for a selectednumber of the subresidual-based tests. Monte Carlosimulation shows that the tests work reasonably wellin finite samples for polynomial and smoothtransition regression models when the block size ischosen by the minimum volatility rule. Inparticular, the subresidual-based tests using theleads-and-lags regression residuals appear to bepromising for empirical work. An empirical examplestudying the U.S. money demand equation illustratesthe use of the tests.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 682 - 709
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

Choi acknowledges financial support from the RGCCompetitive Earmarked Research Grant 2003–2004under Project No. HKUST6223/03H. Saikkonen thanksthe Research Unit of Economic Structures andGrowth (RUESG) in the University of Helsinki andthe Yrjö Jahnsson Foundation for financialsupport. The authors are grateful to Bruce Hansen,Peter Phillips and two anonymous referees fortheir comments on this paper.

References

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