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TESTING STRUCTURAL CHANGE IN PARTIALLY LINEAR 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 for partially linear time-series models. The first tests for structural change in the parametric component, based on the cumulative sums of gradients from a single semiparametric regression. The second tests for structural change in the parametric and nonparametric components simultaneously, based on the cumulative sums of weighted residuals from the same semiparametric regression. We derive the limiting distributions of both tests under the null hypothesis of no structural change and for sequences of local alternatives. We show that the tests are generally not asymptotically pivotal under the null but may be free of nuisance parameters asymptotically under further asymptotic stationarity conditions. Our tests thus complement the conventional instability tests for parametric models. To improve the finite-sample performance of our tests, we also propose a wild bootstrap version of our tests and justify its validity. Finally, we conduct a small set of Monte Carlo simulations to investigate the finite-sample properties of the tests.

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 and two anonymous referees for their many constructive comments on the previous versions of the paper. They also thank Peter Robinson, Rong Chen, Jiti Gao, Yong Zhou, and the participants of FERM 2007 in Beijing and the 2008 International Symposium on Nonlinear Time Series in Xiamen for their valuable comments. The first author gratefully acknowledges financial support from the NSFC under grants 70501001 and 70601001.

References

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