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ESTIMATION AND INFERENCE FOR VARYING-COEFFICIENT MODELS WITH NONSTATIONARY REGRESSORS USING PENALIZED SPLINES

Published online by Cambridge University Press:  14 October 2014

Haiqiang Chen ,
Ying Fang  and
Yingxing Li
Haiqiang Chen
Affiliation:
Xiamen University
Ying Fang*
Affiliation:
Xiamen University
Yingxing Li*
Affiliation:
Xiamen University
*
*Address correspondence to Ying Fang, Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China; e-mail: yifst1@gmail.com; or to: Yingxing Li, Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China; e-mail: yxli@xmu.edu.cn.
*Address correspondence to Ying Fang, Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China; e-mail: yifst1@gmail.com; or to: Yingxing Li, Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China; e-mail: yxli@xmu.edu.cn.
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Abstract

This paper considers estimation and inference for varying-coefficient models with nonstationary regressors. We propose a nonparametric estimation method using penalized splines, which achieves the same optimal convergence rate as kernel-based methods, but enjoys computation advantages. Utilizing the mixed model representation of penalized splines, we develop a likelihood ratio test statistic for checking the stability of the regression coefficients. We derive both the exact and the asymptotic null distributions of this test statistic. We also demonstrate its optimality by examining its local power performance. These theoretical findings are well supported by simulation studies.

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Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 4 , August 2015 , pp. 753 - 777
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

The authors are grateful to Peter Phillips, Wolfgang Härdle, and anonymous referees for their helpful comments. We also thank Zongwu Cai, Jiti Gao, Yongmiao Hong, and all participants of the 3rd WISE-Humboldt Workshop in Nonparametric Nonstationary High-dimensional Econometrics in May 2012. We acknowledge the financial support from the National Science Foundation of China with grant numbers 71201137, 71271179, 71131008, and 11201390, and from the Natural Science Foundation of Fujian Province with grant number 2013J01024, as well as the Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk”.

References

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