IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v10y2017i4p17-d113895.html
   My bibliography  Save this article

GARCH Modelling of Cryptocurrencies

Author

Listed:
  • Jeffrey Chu

    (School of Mathematics, University of Manchester, Manchester M13 9PL, U.K.)

  • Stephen Chan

    (Department of Mathematics and Statistics, American University of Sharjah, Sharjah P.O. Box 26666, UAE)

  • Saralees Nadarajah

    (School of Mathematics, University of Manchester, Manchester M13 9PL, U.K.)

  • Joerg Osterrieder

    (School of Engineering, Zurich University of Applied Sciences, 8400 Winterthur, Switzerland)

Abstract

With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms of five criteria. Conclusions are drawn on the best fitting models, forecasts and acceptability of value at risk estimates.

Suggested Citation

  • Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," JRFM, MDPI, vol. 10(4), pages 1-15, October.
    • Handle: RePEc:gam:jjrfmx:v:10:y:2017:i:4:p:17-:d:113895
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/10/4/17/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/10/4/17/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael McAleer & Christian M. Hafner, 2014. "A One Line Derivation of EGARCH," Econometrics, MDPI, vol. 2(2), pages 1-6, June.
    2. Guillaume Gaetan Martinet & Michael McAleer, 2018. "On the invertibility of EGARCH(p, q)," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 824-849, September.
    3. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    5. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. 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.
    8. Stephen Chan & Jeffrey Chu & Saralees Nadarajah & Joerg Osterrieder, 2017. "A Statistical Analysis of Cryptocurrencies," JRFM, MDPI, vol. 10(2), pages 1-23, May.
    9. 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.
    10. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
    11. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    12. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    13. Gonçalves, E. & Leite, J. & Mendes-Lopes, N., 2012. "On the probabilistic structure of power threshold generalized arch stochastic processes," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1597-1609.
    14. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
    15. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    16. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    17. Chen, Shi & Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Lee, TM & Ong, Bobby, 2016. "A first econometric analysis of the CRIX family," SFB 649 Discussion Papers 2016-031, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    18. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    19. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    20. Christoffersen, Peter & Hahn, Jinyong & Inoue, Atsushi, 2001. "Testing and comparing Value-at-Risk measures," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 325-342, July.
    21. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    22. 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.
    23. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    24. Guglielmo Maria Caporale & Nikitas Pittis & Nicola Spagnolo, 2003. "IGARCH models and structural breaks," Applied Economics Letters, Taylor & Francis Journals, vol. 10(12), pages 765-768.
    25. Bouri, Elie & Azzi, Georges & Dyhrberg, Anne Haubo, 2017. "On the return-volatility relationship in the Bitcoin market around the price crash of 2013," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 11, pages 1-16.
    26. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    27. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    28. Dyhrberg, Anne Haubo, 2016. "Bitcoin, gold and the dollar – A GARCH volatility analysis," Finance Research Letters, Elsevier, vol. 16(C), pages 85-92.
    29. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836.
    30. Jamal Bouoiyour & Refk Selmi, 2016. "Bitcoin: a beginning of a new phase?," Economics Bulletin, AccessEcon, vol. 36(3), pages 1430-1440.
    31. repec:dau:papers:123456789/10571 is not listed on IDEAS
    32. Harald Kinateder & Niklas Wagner, 2014. "Multiple-period market risk prediction under long memory: when VaR is higher than expected," Journal of Risk Finance, Emerald Group Publishing, vol. 15(1), pages 4-32, January.
    33. Bouoiyour, Jamal & Selmi, Refk, 2015. "Bitcoin Price: Is it really that New Round of Volatility can be on way?," MPRA Paper 65580, University Library of Munich, Germany.
    34. Dyhrberg, Anne Haubo, 2016. "Hedging capabilities of bitcoin. Is it the virtual gold?," Finance Research Letters, Elsevier, vol. 16(C), pages 139-144.
    35. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    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. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    4. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    5. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    6. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    7. Cheikh, Nidhaleddine Ben & Zaied, Younes Ben & Chevallier, Julien, 2020. "Asymmetric volatility in cryptocurrency markets: New evidence from smooth transition GARCH models," Finance Research Letters, Elsevier, vol. 35(C).
    8. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    9. Cristina Chinazzo & Vahidin Jeleskovic, 2024. "Forecasting Bitcoin Volatility: A Comparative Analysis of Volatility Approaches," Papers 2401.02049, arXiv.org.
    10. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," Post-Print hal-01943883, HAL.
    11. repec:hal:wpaper:hal-01943883 is not listed on IDEAS
    12. Vahidin Jeleskovic & Mirko Meloni & Zahid Irshad Younas, 2020. "Cryptocurrencies: A Copula Based Approach for Asymmetric Risk Marginal Allocations," MAGKS Papers on Economics 202034, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    13. Gerrit Reher & Bernd Wilfling, 2016. "A nesting framework for Markov-switching GARCH modelling with an application to the German stock market," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 411-426, March.
    14. Panagiotidis, Theodore & Papapanagiotou, Georgios & Stengos, Thanasis, 2022. "On the volatility of cryptocurrencies," Research in International Business and Finance, Elsevier, vol. 62(C).
    15. T. Takaishi, 2021. "Power-Law Return-Volatility Cross Correlations of Bitcoin," Papers 2102.08187, arXiv.org.
    16. Caporale, Guglielmo Maria & Zekokh, Timur, 2019. "Modelling volatility of cryptocurrencies using Markov-Switching GARCH models," Research in International Business and Finance, Elsevier, vol. 48(C), pages 143-155.
    17. Owusu Junior, Peterson & Tiwari, Aviral Kumar & Tweneboah, George & Asafo-Adjei, Emmanuel, 2022. "GAS and GARCH based value-at-risk modeling of precious metals," Resources Policy, Elsevier, vol. 75(C).
    18. Fakhfekh, Mohamed & Jeribi, Ahmed, 2020. "Volatility dynamics of crypto-currencies’ returns: Evidence from asymmetric and long memory GARCH models," Research in International Business and Finance, Elsevier, vol. 51(C).
    19. Baumöhl, Eduard & Lyócsa, Štefan, 2014. "Volatility and dynamic conditional correlations of worldwide emerging and frontier markets," Economic Modelling, Elsevier, vol. 38(C), pages 175-183.
    20. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    21. Nikolaos Antonakakis & Ioannis Chatziantoniou & David Gabauer, 2021. "The impact of Euro through time: Exchange rate dynamics under different regimes," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1375-1408, January.

    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:gam:jjrfmx:v:10:y:2017:i:4:p:17-:d:113895. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.