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Testing the Nullity of GARCH Coefficients : Correction of the Standard Tests and Relative Efficiency Comparisons


  • Christian Francq


  • Jean-Michel Zakoïan



This article is concerned by testing the nullity of coefficients in GARCH models. The problem is nonstandard because the quasi-maximum likelihood estimator is subject to positivity constraints. The paperestablishes the asymptotic null and local alternative distributions of Wald, score, and quasi-likelihood ratiotests. Efficiency comparisons under fixed alternatives are also considered. Two cases of special interestare: (i) tests of the null hypothesis of one coefficient equal to zero and (ii) tests of the null hypothesisof no conditional heteroscedasticity. The results are illustrated by means of simulation experiments. Anempirical application to the Standard & Poor 500 and the CAC40 indexes is proposed.

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  • Christian Francq & Jean-Michel Zakoïan, 2008. "Testing the Nullity of GARCH Coefficients : Correction of the Standard Tests and Relative Efficiency Comparisons," Working Papers 2008-04, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2008-04

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    References listed on IDEAS

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    18. Francq, Christian & Zakoian, Jean-Michel, 2007. "Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1265-1284, September.
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    Cited by:

    1. Rasmus Søndergaard Pedersen & Anders Rahbek, 2017. "Testing Garch-X Type Models," Discussion Papers 17-15, University of Copenhagen. Department of Economics.
    2. Christian Francq & Lajos Horváth & Jean-Michel Zakoïan, 2016. "Variance Targeting Estimation of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(2), pages 353-382.
    3. Ahmed El Ghini & Youssef Saidi, 2017. "Return and volatility spillovers in the Moroccan stock market during the financial crisis," Empirical Economics, Springer, vol. 52(4), pages 1481-1504, June.
    4. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    5. Agosto, Arianna & Cavaliere, Giuseppe & Kristensen, Dennis & Rahbek, Anders, 2016. "Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 640-663.
    6. Francq, Christian & Thieu, Le Quyen, 2015. "Qml inference for volatility models with covariates," MPRA Paper 63198, University Library of Munich, Germany.
    7. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    8. Francq, Christian & Zakoian, Jean-Michel, 2014. "Estimating multivariate GARCH and stochastic correlation models equation by equation," MPRA Paper 54250, University Library of Munich, Germany.
    9. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
    10. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics


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