IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/78126.html
   My bibliography  Save this paper

On the Invertibility of EGARCH(p,q)

Author

Listed:
  • 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, 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

  • Martinet, G.G. & McAleer, M.J., 2015. "On the Invertibility of EGARCH(p,q)," Econometric Institute Research Papers EI 2015-12, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:78126
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/78126/EI2015-12-1-.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. 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.
    5. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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.
    4. Chia-Lin Chang & Michael McAleer & Chien-Hsun Wang, 2017. "An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors," IJFS, MDPI, vol. 6(1), pages 1-24, December.
    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.
    13. repec:hal:wpaper:hal-01943883 is not listed on IDEAS
    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.
    18. 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).
    19. Zhang, Junru & Zhang, Zhaoyong, 2021. "CSR, Media and Stock Illiquidity: Evidence from Chinese Listed Financial Firms," Finance Research Letters, Elsevier, vol. 41(C).
    20. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    3. 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.
    4. 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.
    5. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michael McAleer & Teodosio Pérez-Amaral, 2015. "A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?," Documentos de Trabajo del ICAE 2015-16, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    6. Chang, Chia-Lin & McAleer, Michael, 2019. "The fiction of full BEKK: Pricing fossil fuels and carbon emissions," Finance Research Letters, Elsevier, vol. 28(C), pages 11-19.
    7. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & Maasoumi, Esfandiar & McAleer, Michael & Pérez-Amaral, Teodosio, 2019. "Choosing expected shortfall over VaR in Basel III using stochastic dominance," International Review of Economics & Finance, Elsevier, vol. 60(C), pages 95-113.
    8. Chia-Lin Chang & Michael McAleer, 2017. "The Fiction of Full BEKK," Documentos de Trabajo del ICAE 2017-06, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    9. Chia-Lin Chang & Shu-Han Hsu & Michael McAleer, 2018. "An Event Study Analysis of Political Events, Disasters, and Accidents for Chinese Tourists to Taiwan," Sustainability, MDPI, vol. 10(11), pages 1-77, November.
    10. Chia-Lin Chang & Shu-Han Hsu & Michael McAleer, 2018. "An Event Study of Chinese Tourists to Taiwan," Tinbergen Institute Discussion Papers 18-003/III, Tinbergen Institute.
    11. Michael McAleer & Christian M. Hafner, 2014. "A One Line Derivation of EGARCH," Econometrics, MDPI, vol. 2(2), pages 1-6, June.
    12. David E. Allen & Michael McAleer, 2018. "Theoretical and Empirical Differences between Diagonal and Full BEKK for Risk Management," Energies, MDPI, vol. 11(7), pages 1-19, June.
    13. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    14. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2018. "Connecting VIX and Stock Index ETF with VAR and Diagonal BEKK," JRFM, MDPI, vol. 11(4), pages 1-25, September.
    15. Chang, Chia-Lin & Jiménez-Martín, Juan-Ángel & Maasoumi, Esfandiar & Pérez-Amaral, Teodosio, 2015. "A stochastic dominance approach to financial risk management strategies," Journal of Econometrics, Elsevier, vol. 187(2), pages 472-485.
    16. Chang, Chia-Lin & Hsu, Hui-Kuang & McAleer, Michael, 2014. "The impact of China on stock returns and volatility in the Taiwan tourism industry," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 381-401.
    17. 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.
    18. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    19. 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.
    20. Jukka Ilomäki & Hannu Laurila & Michael McAleer, 2018. "Asymmetric Risk Impacts of Chinese Tourists to Taiwan," Documentos de Trabajo del ICAE 2018-05, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ems:eureir:78126. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.