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A Nonparametric Distribution-Free Test for Serial Independence of Errors

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  • Zaichao Du
  • Juan Carlos Escanciano

Abstract

In this article, we propose a test for the serial independence of unobservable errors in location-scale models. We consider a Hoeffding-Blum-Kiefer-Rosenblat type empirical process applied to residuals, and show that under certain conditions it converges weakly to the same limit as the process based on true errors. We then consider a generalized spectral test applied to estimated residuals, and get a test that is asymptotically distribution-free and powerful against any type of pairwise dependence at all lags. Some Monte Carlo simulations validate our theoretical findings.

Suggested Citation

  • Zaichao Du & Juan Carlos Escanciano, 2015. "A Nonparametric Distribution-Free Test for Serial Independence of Errors," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1011-1034, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:1011-1034
    DOI: 10.1080/07474938.2014.956616
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    References listed on IDEAS

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    1. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    2. Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
    3. Escanciano, J. Carlos, 2007. "Weak convergence of non-stationary multivariate marked processes with applications to martingale testing," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1321-1336, August.
    4. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    5. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.
    6. Tianxi Cai & Lu Tian & Scott D. Solomon & L.J. Wei, 2008. "Predicting future responses based on possibly mis-specified working models," Biometrika, Biometrika Trust, vol. 95(1), pages 75-92.
    7. Bravo, Francesco & Chu, Ba M. & Jacho-Chávez, David T., 2017. "Generalized empirical likelihood M testing for semiparametric models with time series data," Econometrics and Statistics, Elsevier, vol. 4(C), pages 18-30.
    8. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
    9. Yongmiao Hong, 2000. "Generalized spectral tests for serial dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 557-574.
    10. Bravo, Francesco, 2009. "Two-step generalised empirical likelihood inference for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1412-1431, August.
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    Cited by:

    1. Kilani Ghoudi & Bruno Rémillard, 2018. "Serial independence tests for innovations of conditional mean and variance models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 3-26, March.

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