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A NONPARAMETRIC GOODNESS-OF-FIT-BASED TEST FOR CONDITIONAL HETEROSKEDASTICITY

Published online by Cambridge University Press:  06 July 2012

Liangjun Su  and
Aman Ullah
Liangjun Su*
Affiliation:
Singapore Management University
Aman Ullah
Affiliation:
University of California, Riverside
*
*Address correspondence to Liangjun Su, School of Economics, Singapore Management University 90 Stanford Road, Singapore 178903; e-mail: ljsu@smu.edu.sg.
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Abstract

In this paper we propose a new nonparametric test for conditional heteroskedasticity based on a measure of nonparametric goodness-of-fit (R2) that is obtained from the local polynomial regression of the residuals from a parametric regression on some covariates. We show that after being appropriately standardized, the nonparametric R2 is asymptotically normally distributed under the null hypothesis and a sequence of Pitman local alternatives. We also prove the consistency of the test and propose a bootstrap method to obtain the bootstrap p-values. We conduct a small set of simulations and compare our test with some popular parametric and nonparametric tests in the literature.

Type
MISCELLANEA
Information
Econometric Theory , Volume 29 , Issue 1 , February 2013 , pp. 187 - 212
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

We sincerely thank the co-editor, Yoon-Jae Whang, and two anonymous referees for their constructive suggestions and comments that have led to a substantial improvement of the paper. We also thank the participants at the 2010 International Symposium on Econometric Theory and Applications (SETA 2010), the 2010 Econometric Society World Congress (ESWC 2010), the Rimini Conference on Economics and Finance (RCEF 2010), the 2011 Summer International Econometrics Symposium at SUFE, Chengdu, and the seminars at West Virginia and McGill Universities, all of whom provided valuable suggestions and discussion. The second author acknowledges financial support from the academic senate, UCR.

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