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Serial independence tests for innovations of conditional mean and variance models

Author

Listed:
  • Kilani Ghoudi

    (United Arab Emirates University)

  • Bruno Rémillard

    (HEC Montréal)

Abstract

In this paper, one studies the asymptotic behavior of empirical processes based on consecutive residuals of univariate conditional mean and variance models. These processes are then used to develop tests of serial independence of the innovations. Even if the limiting distributions of the empirical processes depend on unknown parameters, it is shown that a Monte Carlo method based on the so-called multipliers can be applied to estimate the P values of the proposed test statistics. A simulation study is carried out to demonstrate the effectiveness of the proposed tests and the behavior of the statistics is also studied under contiguous alternatives.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-016-0521-3
    DOI: 10.1007/s11749-016-0521-3
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    References listed on IDEAS

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    1. Zaichao Du, 2016. "Nonparametric bootstrap tests for independence of generalized errors," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 55-83, February.
    2. Genest, Christian & Ghoudi, Kilani & Remillard, Bruno, 2007. "Rank-Based Extensions of the Brock, Dechert, and Scheinkman Test," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1363-1376, December.
    3. Berkes, István & Horváth, Lajos & Kokoszka, Piotr, 2003. "Asymptotics For Garch Squared Residual Correlations," Econometric Theory, Cambridge University Press, vol. 19(4), pages 515-540, August.
    4. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    5. W. K. Li & T. K. Mak, 1994. "On The Squared Residual Autocorrelations In Non‐Linear Time Series With Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 627-636, November.
    6. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    7. Andreou, Elena & Werker, Bas J.M., 2015. "Residual-based rank specification tests for AR–GARCH type models," Journal of Econometrics, Elsevier, vol. 185(2), pages 305-331.
    8. Ghoudi, Kilani & Rémillard, Bruno, 2014. "Comparison of specification tests for GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 291-300.
    9. Ke. Zhu, 2013. "A mixed portmanteau test for ARMA-GARCH models by the quasi-maximum exponential likelihood estimation approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 230-237, March.
    10. Heung Wong & Shiqing Ling, 2005. "Mixed Portmanteau Tests for Time‐Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 569-579, July.
    11. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
    12. 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.
    13. Miguel A. Delgado, 1996. "Testing Serial Independence Using The Sample Distribution Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(3), pages 271-285, May.
    14. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
    15. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
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    Cited by:

    1. Nasri, Bouchra R. & Rémillard, Bruno N. & Bouezmarni, Taoufik, 2019. "Semi-parametric copula-based models under non-stationarity," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 347-365.
    2. S. G. Meintanis & M. Hušková & M. D. Jiménez-Gamero, 2018. "Editorial," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-2, March.
    3. Nasri, Bouchra R. & Rémillard, Bruno N. & Bahraoui, Tarik, 2022. "Change-point problems for multivariate time series using pseudo-observations," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    4. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    5. M. Dolores Jiménez-Gamero & Sangyeol Lee & Simos G. Meintanis, 2020. "Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 682-703, September.

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