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TESTING STRUCTURAL CHANGE IN PARTIALLYLINEAR MODELS

Published online by Cambridge University Press:  22 March 2010

Liangjun Su  and
Halbert White
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Abstract

We consider two tests of structural change forpartially linear time-series models. The first testsfor structural change in the parametric component,based on the cumulative sums of gradients from asingle semiparametric regression. The second testsfor structural change in the parametric andnonparametric components simultaneously, based onthe cumulative sums of weighted residuals from thesame semiparametric regression. We derive thelimiting distributions of both tests under the nullhypothesis of no structural change and for sequencesof local alternatives. We show that the tests aregenerally not asymptotically pivotal under the nullbut may be free of nuisance parametersasymptotically under further asymptotic stationarityconditions. Our tests thus complement theconventional instability tests for parametricmodels. To improve the finite-sample performance ofour tests, we also propose a wild bootstrap versionof our tests and justify its validity. Finally, weconduct a small set of Monte Carlo simulations toinvestigate the finite-sample properties of thetests.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1761 - 1806
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

The authors gratefully thank Oliver Linton andtwo anonymous referees for their many constructivecomments on the previous versions of the paper.They also thank Peter Robinson, Rong Chen, JitiGao, Yong Zhou, and the participants of FERM 2007in Beijing and the 2008 International Symposium onNonlinear Time Series in Xiamen for their valuablecomments. The first author gratefully acknowledgesfinancial support from the NSFC under grants70501001 and 70601001.

References

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