IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v41y2020i2p341-350.html
   My bibliography  Save this article

On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model

Author

Listed:
  • Stelios Arvanitis
  • Sofia Anyfantaki

Abstract

We derive the limit theory of the Gaussian stable quasi maximum likelihood estimator for the stationary EGARCH(1,1) model when the squared innovation process has marginals with regularly varying tails. We derive regularly varying rates and limiting stable distributions. We perform Monte Carlo experiments to assess the extent of the parameter space corresponding to the invertibility condition, and the quality of the asymptotic approximation.

Suggested Citation

  • Stelios Arvanitis & Sofia Anyfantaki, 2020. "On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 341-350, March.
    • Handle: RePEc:bla:jtsera:v:41:y:2020:i:2:p:341-350
    DOI: 10.1111/jtsa.12494
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12494
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12494?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Arvanitis, Stelios & Louka, Alexandros, 2017. "Stable limits for the Gaussian QMLE in the non-stationary GARCH(1,1) model," Economics Letters, Elsevier, vol. 161(C), pages 135-137.
    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. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    4. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    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.
    Full references (including those not matched with items on IDEAS)

    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. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    2. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, September.
    3. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    4. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    5. Das, Suman & Roy, Saikat Sinha, 2023. "Following the leaders? A study of co-movement and volatility spillover in BRICS currencies," Economic Systems, Elsevier, vol. 47(2).
    6. Tinkl, Fabian, 2010. "Asymptotic theory for M estimators for martingale differences with applications to GARCH models," FAU Discussion Papers in Economics 09/2010, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    7. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    8. Meister, Alexander & Kreiß, Jens-Peter, 2016. "Statistical inference for nonparametric GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3009-3040.
    9. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 319-342.
    10. Lopes, Sílvia R.C. & Prass, Taiane S., 2014. "Theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 278-307.
    11. Arvanitis, Stelios, 2019. "Stable limit theory for the Gaussian QMLE in a non-stationary asymmetric GARCH model," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 166-172.
    12. Wang, Chuan-Sheng & Zhao, Zhibiao, 2016. "Conditional Value-at-Risk: Semiparametric estimation and inference," Journal of Econometrics, Elsevier, vol. 195(1), pages 86-103.
    13. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    14. Li, Dong & Li, Muyi & Wu, Wuqing, 2014. "On dynamics of volatilities in nonstationary GARCH models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 86-90.
    15. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    16. Arvanitis, Stelios & Louka, Alexandros, 2016. "A CLT for martingale transforms with infinite variance," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 116-123.
    17. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    18. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    19. So, Mike K.P. & Chung, Ray S.W., 2015. "Statistical inference for conditional quantiles in nonlinear time series models," Journal of Econometrics, Elsevier, vol. 189(2), pages 457-472.
    20. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.

    More about this item

    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:bla:jtsera:v:41:y:2020:i:2:p:341-350. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.