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On the Invertibility of EGARCH(p,q)

Author

Listed:
  • Guillaume Gaetan Martinet

    (ENSAE Paris Tech, France
    Department of Industrial Engineering and Operations Research Columbia University, USA)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute, The Netherlands, Department of Quantitative Economics, Complutense University of Madrid, and Institute of Economic Research, Kyoto University.)

Abstract

Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH(p,q) model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH(p,q) parameters.

Suggested Citation

  • Guillaume Gaetan Martinet & Michael McAleer, 2015. "On the Invertibility of EGARCH(p,q)," Documentos de Trabajo del ICAE 2015-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:1503
    Note: The authors are grateful to the Editor-in-Chief, Rob Taylor, an Associate Editor and two referees for very helpful comments and suggestions, and to Christian Hafner for insightful discussions. For financial support, the first author wishes to thank the National Science Council, Taiwan, and the second author is most grateful to the Australian Research Council and the National Science Council, Taiwan.
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    References listed on IDEAS

    as
    1. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
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    7. Olivier Wintenberger, 2013. "Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 846-867, December.
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    Cited by:

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    8. Asai, M. & McAleer, M.J., 2016. "Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes," Econometric Institute Research Papers EI2016-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Chang, Chia-Lin & McAleer, Michael, 2017. "The correct regularity condition and interpretation of asymmetry in EGARCH," Economics Letters, Elsevier, vol. 161(C), pages 52-55.
    10. Chang, C-L. & McAleer, M.J. & Wang, Y-A., 2016. "Modelling Volatility Spillovers for Bio-ethanol, Sugarcane and Corn," Econometric Institute Research Papers EI2016-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Chia-Lin Chang & Yiying Li & Michael McAleer, 2018. "Volatility Spillovers between Energy and Agricultural Markets: A Critical Appraisal of Theory and Practice," Energies, MDPI, vol. 11(6), pages 1-19, June.
    12. Blasques, Francisco & van Brummelen, Janneke & Gorgi, Paolo & Koopman, Siem Jan, 2024. "Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions," Journal of Econometrics, Elsevier, vol. 238(1).
    13. You-How Go & Wee-Yeap Lau, 2020. "Does Trading Volume explain the Information Flow of Crude Palm Oil Futures Returns?," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 12(2), pages 115-136, December.
    14. Urom, Christian & Onwuka, Kevin O. & Uma, Kalu E. & Yuni, Denis N., 2020. "Regime dependent effects and cyclical volatility spillover between crude oil price movements and stock returns," International Economics, Elsevier, vol. 161(C), pages 10-29.
    15. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    16. Zhang, Junru & Zhang, Zhaoyong, 2021. "CSR, Media and Stock Illiquidity: Evidence from Chinese Listed Financial Firms," Finance Research Letters, Elsevier, vol. 41(C).
    17. Onur Özdemir, 2022. "Cue the volatility spillover in the cryptocurrency markets during the COVID-19 pandemic: evidence from DCC-GARCH and wavelet analysis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-38, December.
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    20. Dey, Asim K. & Hoque, G.M. Toufiqul & Das, Kumer P. & Panovska, Irina, 2022. "Impacts of COVID-19 local spread and Google search trend on the US stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).

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    More about this item

    Keywords

    Leverage; asymmetry; Existence; Stochastic process; Asymptotic properties; Invertibility.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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