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A Nonparametric Goodness-Of-Fit-Based Test For Conditional Heteroskedasticity

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  • Su, Liangjun
  • Ullah, Aman

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.

Suggested Citation

  • Su, Liangjun & Ullah, Aman, 2013. "A Nonparametric Goodness-Of-Fit-Based Test For Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 29(1), pages 187-212, February.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:01:p:187-212_00
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    Cited by:

    1. Su, Liangjun & Jin, Sainan & Zhang, Yonghui, 2015. "Specification test for panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 186(1), pages 222-244.
    2. Yan Li & Liangjun Su & Yuewu Xu, 2015. "A Combined Approach to the Inference of Conditional Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-220, April.
    3. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    4. Fu, Zhonghao & Hong, Yongmiao & Su, Liangjun & Wang, Xia, 2023. "Specification tests for time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 235(2), pages 720-744.
    5. Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, vol. 1(2), pages 1-23, September.
    6. Liangjun Su & Stefan Hoderlein & Halbert White, 2013. "Testing Monotonicity in Unobservables with Panel Data," Boston College Working Papers in Economics 892, Boston College Department of Economics, revised 01 Feb 2016.
    7. Hu, Yue & Li, Haiqi & Tan, Falong, 2024. "Testing the parametric form of the conditional variance in regressions based on distance covariance," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    8. Li, Zhaoyuan & Yao, Jianfeng, 2019. "Testing for heteroscedasticity in high-dimensional regressions," Econometrics and Statistics, Elsevier, vol. 9(C), pages 122-139.
    9. Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.

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