IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v27y2018i1d10.1007_s11749-016-0506-2.html
   My bibliography  Save this article

Goodness-of-fit tests for Log-GARCH and EGARCH models

Author

Listed:
  • Christian Francq

    (CREST and University of Lille)

  • Olivier Wintenberger

    (Universities of Paris 6 and Copenhagen, LSTA)

  • Jean-Michel Zakoïan

    (CREST and University of Lille)

Abstract

This paper studies goodness-of-fit tests and specification tests for an extension of the Log-GARCH model, which is both asymmetric and stable by scaling. A Lagrange-multiplier test is derived for testing the extended Log-GARCH against more general formulations taking the form of combinations of Log-GARCH and exponential GARCH (EGARCH). The null assumption of an EGARCH is also tested. Portmanteau goodness-of-fit tests are developed for the extended Log-GARCH. An application to real financial data is proposed.

Suggested Citation

  • Christian Francq & Olivier Wintenberger & Jean-Michel Zakoïan, 2018. "Goodness-of-fit tests for Log-GARCH and EGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 27-51, March.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-016-0506-2
    DOI: 10.1007/s11749-016-0506-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-016-0506-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-016-0506-2?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    3. 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.
    4. W. K. Li & T. K. Mak, 1994. "On The Squared Residual Autocorrelations In Non‐Linear Time Series With Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 627-636, November.
    5. 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.
    6. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
    7. repec:dau:papers:123456789/10571 is not listed on IDEAS
    8. Anne Leucht & Jens-Peter Kreiss & Michael H. Neumann, 2015. "A Model Specification Test For GARCH(1,1) Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1167-1193, December.
    9. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    10. Escanciano, J. Carlos, 2010. "Asymptotic Distribution-Free Diagnostic Tests For Heteroskedastic Time Series Models," Econometric Theory, Cambridge University Press, vol. 26(3), pages 744-773, June.
    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. Christian M. Dahl & Emma M. Iglesias, 2021. "Asymptotic normality of the MLE in the level-effect ARCH model," Statistical Papers, Springer, vol. 62(1), pages 117-135, February.
    2. S. G. Meintanis & M. Hušková & M. D. Jiménez-Gamero, 2018. "Editorial," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-2, March.
    3. Rewat Khanthaporn, 2022. "Analysis of Nonlinear Comovement of Benchmark Thai Government Bond Yields," PIER Discussion Papers 183, Puey Ungphakorn Institute for Economic Research.
    4. Pourkhanali, Armin & Tafakori, Laleh & Bee, Marco, 2023. "Forecasting Value-at-Risk using functional volatility incorporating an exogenous effect," International Review of Financial Analysis, Elsevier, vol. 89(C).
    5. Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for the asymmetric power GARCH model when the power is unknown," Statistical Papers, Springer, vol. 63(3), pages 755-793, June.
    6. M. Dolores Jiménez-Gamero & Sangyeol Lee & Simos G. Meintanis, 2020. "Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 682-703, September.

    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. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Oxford University Press, vol. 16(1), pages 129-154.
    2. Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.
    3. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    4. Sucarrat, Genaro, 2018. "The Log-GARCH Model via ARMA Representations," MPRA Paper 100386, University Library of Munich, Germany.
    5. Bonnier, Jean-Baptiste, 2022. "Forecasting crude oil volatility with exogenous predictors: As good as it GETS?," Energy Economics, Elsevier, vol. 111(C).
    6. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    7. Escribano, Alvaro & Sucarrat, Genaro, 2018. "Equation-by-equation estimation of multivariate periodic electricity price volatility," Energy Economics, Elsevier, vol. 74(C), pages 287-298.
    8. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. Sucarrat, Genaro & Escribano, Alvaro, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," MPRA Paper 50699, University Library of Munich, Germany.
    10. Charles, Amélie & Darné, Olivier, 2017. "Forecasting crude-oil market volatility: Further evidence with jumps," Energy Economics, Elsevier, vol. 67(C), pages 508-519.
    11. Francq, Christian & Sucarrat, Genaro, 2017. "An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 16-32.
    12. Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for the asymmetric power GARCH model when the power is unknown," Statistical Papers, Springer, vol. 63(3), pages 755-793, June.
    13. Rewat Khanthaporn, 2022. "Analysis of Nonlinear Comovement of Benchmark Thai Government Bond Yields," PIER Discussion Papers 183, Puey Ungphakorn Institute for Economic Research.
    14. Xu, Yongdeng, 2024. "Extended multivariate EGARCH model: A model for zero†return and negative spillovers," Cardiff Economics Working Papers E2024/24, Cardiff University, Cardiff Business School, Economics Section.
    15. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effect in Financial Returns," Documents de travail du Centre d'Economie de la Sorbonne 14022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    16. Chorro, Christophe & Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2018. "Testing for leverage effects in the returns of US equities," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 290-306.
    17. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2017. "Testing for Leverage Effects in the Returns of US Equities," Post-Print halshs-00973922, HAL.
    18. Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," JRFM, MDPI, vol. 10(4), pages 1-15, October.
    19. Carnero, M. Angeles & Pérez, Ana, 2019. "Leverage effect in energy futures revisited," Energy Economics, Elsevier, vol. 82(C), pages 237-252.
    20. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.

    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:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-016-0506-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.