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Inference on Multiplicative Component GARCH without any Small-Order Moment

Author

Listed:
  • Christian Francq

    (CREST-ENSAE and University of Lille)

  • Baye Matar Kandji

    (CREST-ENSAE)

  • Jean-Michel Zakoian

    (University of Lille and CREST-ENSAE)

Abstract

In multiplicative component GARCH models, the volatility is decomposed into the product of two factors which often received interpretations in terms of "short run" (high frequency) and "long run" (low frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order nite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the Quasi-Maximum Likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real nancial data.

Suggested Citation

  • Christian Francq & Baye Matar Kandji & Jean-Michel Zakoian, 2022. "Inference on Multiplicative Component GARCH without any Small-Order Moment," Working Papers 2022-09, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2022-09
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    References listed on IDEAS

    as
    1. Christian Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    2. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
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    5. Francq, Christian & Horvath, Lajos & Zakoïan, Jean-Michel, 2010. "Sup-Tests For Linearity In A General Nonlinear Ar(1) Model," Econometric Theory, Cambridge University Press, vol. 26(4), pages 965-993, August.
    6. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836.
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    More about this item

    Keywords

    GARCH-MIDAS; Moments existence; QMLE; Residual Bootstrap; Tests on boundary parameters.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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