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A CONSISTENT NONPARAMETRIC TEST ON SEMIPARAMETRIC SMOOTH COEFFICIENT MODELS WITH INTEGRATED TIME SERIES

Published online by Cambridge University Press:  24 February 2015

Yiguo Sun ,
Zongwu Cai  and
Qi Li
Yiguo Sun
Affiliation:
University of Guelph
Zongwu Cai*
Affiliation:
University of Kansas and Xiamen University
Qi Li
Affiliation:
Texas A&M University and Capital University of Economics and Business
*
*Address correspondence to Zongwu Cai, Department of Economics, University of Kansas, Lawrence, KS 66045, USA; e-mail: [email protected].
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Abstract

In this paper, we propose a simple nonparametric test for testing the null hypothesis of constant coefficients against nonparametric smooth coefficients in a semiparametric varying coefficient model with integrated time series. We establish the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Moreover, we derive a central limit theorem for a degenerate second order U-statistic, which contains a mixture of stationary and nonstationary variables and is weighted locally on a stationary variable. This result is of independent interest and useful in other applications. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed test.

Type
MISCELLANEA
Information
Econometric Theory , Volume 32 , Issue 4 , August 2016 , pp. 988 - 1022
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

We thank the anonymous referees, Peter Phillips and Qiying Wang for their insightful comments that greatly improved our paper. Sun’s research is supported by the Social Sciences and Humanities Research Council of Canada (SSHRC) grant 410-2009-0109. Cai’s research is supported, in part, by the National Nature Science Foundation of China grants #71131008 (Key Project) and #70971113. Li’s research is partially supported by the National Nature Science Foundation of China grant #71133001.

References

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