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On the Invertibility of EGARCH

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  • Martinet, G.G.
  • McAleer, M.J.

Abstract

__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. A limitation in the development of asymptotic properties of the QMLE for EGARCH is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH 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 parameters.

Suggested Citation

  • Martinet, G.G. & McAleer, M.J., 2014. "On the Invertibility of EGARCH," Econometric Institute Research Papers EI2014-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:51750
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Michael McAleer & Christian M. Hafner, 2014. "A One Line Derivation of EGARCH," Econometrics, MDPI, vol. 2(2), pages 1-6, June.
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    5. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    6. 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.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

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    2. 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.
    3. 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.
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    5. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," Post-Print hal-01943883, HAL.
    6. 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).
    7. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    8. Rangan Gupta & Chi Keung Marco Lau & Seong-Min Yoon, 2019. "OPEC News Announcement Effect on Volatility in the Crude Oil Market: A Reconsideration," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(4), pages 1-23, December.
    9. Chang, Chia-Lin & McAleer, Michael & Wang, Yu-Ann, 2018. "Modelling volatility spillovers for bio-ethanol, sugarcane and corn spot and futures prices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1002-1018.
    10. Manabu Asai & Chia-Lin Chang & Michael McAleer, 2016. "Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers," Tinbergen Institute Discussion Papers 16-076/III, Tinbergen Institute.
    11. Chia-Lin Chang & Michael McAleer & Yu-Ann Wang, 2016. "Modelling volatility spillovers for bio-ethanol, sugarcane and corn," Documentos de Trabajo del ICAE 2016-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    12. Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," JRFM, MDPI, vol. 10(4), pages 1-15, October.
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    14. Manabu Asai & Michael McAleer, 2016. "Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes," Documentos de Trabajo del ICAE 2016-14, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    15. Xiaoyi Shen & Albert K. Tsui & Zhaoyong Zhang, 2019. "Volatility Timing in CPF Investment Funds in Singapore: Do They Outperform Non-CPF Funds?," Risks, MDPI, vol. 7(4), pages 1-16, October.
    16. Junru Zhang & Hadrian Geri Djajadikerta & Zhaoyong Zhang, 2018. "Does Sustainability Engagement Affect Stock Return Volatility? Evidence from the Chinese Financial Market," Sustainability, MDPI, vol. 10(10), pages 1-21, September.
    17. 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.
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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
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • 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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