Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T04:27:39.481Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected].
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Andrews, D.W.K. (1995) Nonparametric kernel estimation for semiparametric models. Econometric Theory 11, 560–596.CrossRefGoogle Scholar
Bernstein, D.S. (2005) Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory. Princeton University Press.Google Scholar
Breusch, T.S. & Pagan, A.R. (1979) A simple test for heteroskedasticity and random variation. Econometrica 47, 1287–1294.CrossRefGoogle Scholar
Chen, S.X. & Gao, J. (2007) An adaptive empirical likelihood test for parametric time series regression models. Journal of Econometrics 141, 950–972.CrossRefGoogle Scholar
De Jong, P. (1987) A central limit theorem for generalized quadratic forms. Probability Theory and Related Fields 75, 261–277.CrossRefGoogle Scholar
Gao, J. (2007)Nonlinear Time Series: Semiparametric and Nonparametric Methods. Chapman & Hall/CRC.CrossRefGoogle Scholar
Giné, E. & Zinn, J. (1990) Bootstrapping general empirical measures. Annals of Probability 18, 851–869.CrossRefGoogle Scholar
Glejser, H. (1969) A new test for heteroskedasticity. Journal of the American Statistical Association 64, 316–323.CrossRefGoogle Scholar
Godfrey, L.G. (1978) Testing for multiplicative heteroskedasticity. Journal of Econometrics 8, 227–236.CrossRefGoogle Scholar
Goldfeld, S.M. & Quandt, R.E. (1965) Some tests for homoskedasticity. Journal of the American Statistical Association 60, 539–547.CrossRefGoogle Scholar
Greene, W.H. (2000) Econometric Analysis, 4th ed. Prentice-Hall.Google Scholar
Hansen, B.E. (2000) Testing for structural change in conditional models. Journal of Econometrics 97, 93–115.Google Scholar
Hansen, B.E. (2008) Uniform convergence rates for kernel estimation with dependent data. Econometric Theory 24, 726–748.CrossRefGoogle Scholar
Hong, Y. (1993) Consistent Testing for Heteroskedasticity of Unknown Form. Manuscript, Department of Economics, Cornell University.Google Scholar
Horowitz, J.L. & Spokoiny, V.G. (2001) An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–631.CrossRefGoogle Scholar
Hsiao, C. & Li, Q. (2001) A consistent test for conditional heteroskedasticity in time-series regression models. Econometric Theory 17, 188–221.Google Scholar
Huang, L.-H. & Chen, J. (2008) Analysis of variance, coefficient of determination and F-test for local polynomial regression. Annals of Statistics 36, 2085–2109.CrossRefGoogle Scholar
Koenker, R. & Bassett, G. (1982) Robust tests for heteroskedasticity based on quantiles. Econometrica 50, 159–171.CrossRefGoogle Scholar
Li, D., Lu, Z., & Linton, O. (2012) Local linear fitting under near epoch dependence: Uniform consistency with convergence rates. Econometric Theory 28, 935–958.CrossRefGoogle Scholar
Li, Q., Hsiao, C., & Zinn, J. (2003) Consistent specification tests for semiparametric/nonparametric models based on series estimation method. Journal of Econometrics 112, 295–325.CrossRefGoogle Scholar
Masry, E. (1996) Multivariate local polynomial regression for time series: Uniform strong consistency rates. Journal of Time Series Analysis 17, 571–599.CrossRefGoogle Scholar
Neumann, M.H. & Paparoditis, E. (2000) On bootstrapping L 2-type statistics in density testing. Statistics & Probability Letters 50, 137–147.CrossRefGoogle Scholar
Newey, W. & Powell, J. (1987) Asymmetric least squares estimation and testing. Econometrica 55, 819–847.CrossRefGoogle Scholar
Pagan, A.R. & Pak, Y. (1993) Testing for heteroskedasticity. In Maddala, G.S., Rao, C.R., & Vinod, H.D. (eds.), Handbook of Statistics, vol. 11, pp. 489–518. Elsevier Science Publishers.Google Scholar
Su, L. & Ullah, A. (2009) Testing conditional uncorrelatedness. Journal of Business & Economic Statistics 27, 18–29.CrossRefGoogle Scholar
Su, L. & White, H. (2010) Testing structural change in partially linear models. Econometric Theory 26, 1761–1806.Google Scholar
White, H. (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 452–475.CrossRefGoogle Scholar
White, H. & Domowitz, I. (1984) Nonlinear regression with dependent observations. Econometrica 52, 143–161.Google Scholar
Yoshihara, K. (1992) Limiting behavior of generalized quadratic forms generated by regular sequences III. Yokohama Mathematical 40, 1–9.Google Scholar
Zheng, X. (2006) Testing Heteroscedasticity in Nonlinear and Nonparametric Regressions with an Application to Interest Rate Volatility. Manuscript, School of Economics, Shanghai Jiaotong University.Google Scholar