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Goodness-of-fit testing of error distribution in nonparametric ARCH(1) models

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  • Koul, Hira L.
  • Zhu, Xiaoqing

Abstract

This paper discusses the goodness-of-fit testing of an error distribution in a nonparametric autoregressive conditionally heteroscedastic model of order one. The test is based on a weighted empirical distribution function of the residuals, where the residuals are obtained from a local linear fit for the autoregressive and heteroscedasticity functions, and the weights are chosen to adjust for the undesirable behavior of these nonparametric estimators in the tails of their domains. An asymptotically distribution free test is obtained via the Khmaladze martingale transformation. A simulation study is included to assess the finite sample level and power behavior of this test. It exhibits some superiority of this test compared to the classical Kolmogorov–Smirnov and Cramér–von Mises tests in terms of the finite sample level and power.

Suggested Citation

  • Koul, Hira L. & Zhu, Xiaoqing, 2015. "Goodness-of-fit testing of error distribution in nonparametric ARCH(1) models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 141-160.
    • Handle: RePEc:eee:jmvana:v:137:y:2015:i:c:p:141-160
    DOI: 10.1016/j.jmva.2015.02.009
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    References listed on IDEAS

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    1. Neumeyer, N. & Van Keilegom, I., 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," LIDAM Reprints ISBA 2010006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Natalie Neumeyer & Leonie Selk, 2013. "A note on non-parametric testing for Gaussian innovations in AR–ARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 362-367, May.
    3. Yao, Qiwei & Tong, Howell, 1994. "Quantifying the influence of initial values on nonlinear prediction," LSE Research Online Documents on Economics 19426, London School of Economics and Political Science, LSE Library.
    4. Wu, Wei Biao & Huang, Yinxiao & Huang, Yibi, 2010. "Kernel estimation for time series: An asymptotic theory," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2412-2431, December.
    5. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    6. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    7. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    8. Leonie Selk & Natalie Neumeyer, 2013. "Testing for a Change of the Innovation Distribution in Nonparametric Autoregression: The Sequential Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 770-788, December.
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    Cited by:

    1. Neumeyer, Natalie & Omelka, Marek & Hudecová, Šárka, 2019. "A copula approach for dependence modeling in multivariate nonparametric time series," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 139-162.
    2. Jiwoong Kim, 2020. "Implementation of a goodness-of-fit test through Khmaladze martingale transformation," Computational Statistics, Springer, vol. 35(4), pages 1993-2017, December.

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