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Kernel-based testing with skewed and heavy-tailed data: Evidence from a nonparametric test for heteroskedasticity

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  • Henderson, Daniel J.
  • Sheehan, Alice

Abstract

We examine the performance of a nonparametric kernel-based specification test in the presence of skewed and heavy-tailed regressors. We start by modifying the Zheng (2009) test for heteroskedasticity by removing the random denominator in the test statistic, a common source of distortion for such tests. Asymptotic equivalence of our test statistic is shown and Monte Carlo simulations are provided to assess the finite sample performance. With normally distributed errors, we find slight improvements using our modified test when the regressors are asymmetric or symmetric without heavy-tails. Trimming and using a smaller bandwidth also improves size for these distributions. When the errors are heavy-tailed, the results are more favorable to our test.

Suggested Citation

  • Henderson, Daniel J. & Sheehan, Alice, 2018. "Kernel-based testing with skewed and heavy-tailed data: Evidence from a nonparametric test for heteroskedasticity," Economics Letters, Elsevier, vol. 172(C), pages 8-11.
    • Handle: RePEc:eee:ecolet:v:172:y:2018:i:c:p:8-11
    DOI: 10.1016/j.econlet.2018.08.007
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    References listed on IDEAS

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    1. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
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    4. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    5. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2012. "n-uniformly consistent density estimation in nonparametric regression models," Journal of Econometrics, Elsevier, vol. 167(2), pages 305-316.
    6. Hsiao, Cheng & Li, Qi, 2001. "A Consistent Test For Conditional Heteroskedasticity In Time-Series Regression Models," Econometric Theory, Cambridge University Press, vol. 17(1), pages 188-221, February.
    7. Henderson Daniel J. & Parmeter Christopher F., 2017. "Root-n Consistent Kernel Density Estimation in Practice," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-10, January.
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    Cited by:

    1. Wang, Wenju & Wang, Qiao, 2019. "Consistent specification test for partially linear models with the k-nearest-neighbor method," Economics Letters, Elsevier, vol. 177(C), pages 89-93.
    2. Huang, Ta-Cheng & Li, Hongjun & Li, Zheng, 2020. "A modified bootstrap for kernel-based specification test with heavy-tailed data," Economics Letters, Elsevier, vol. 189(C).

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    More about this item

    Keywords

    Heteroskedasticity; Kernel; Kurtosis; Skewness; Specification testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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