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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    4. Michael McAleer & Christian M. Hafner, 2014. "A One Line Derivation of EGARCH," Econometrics, MDPI, vol. 2(2), pages 1-6, June.
    5. Shi Chen & Cathy Yi-Hsuan Chen & Wolfgang Karl Härdle & TM Lee & Bobby Ong, 2016. "A first econometric analysis of the CRIX family," SFB 649 Discussion Papers SFB649DP2016-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    13. 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.
    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. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    20. 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.
    21. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    22. 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.
    23. Stephen Chan & Jeffrey Chu & Saralees Nadarajah & Joerg Osterrieder, 2017. "A Statistical Analysis of Cryptocurrencies," JRFM, MDPI, vol. 10(2), pages 1-23, May.
    24. 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.
    25. 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.
    26. 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.
    27. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    28. 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.
    29. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    30. Dyhrberg, Anne Haubo, 2016. "Bitcoin, gold and the dollar – A GARCH volatility analysis," Finance Research Letters, Elsevier, vol. 16(C), pages 85-92.
    31. Jamal Bouoiyour & Refk Selmi, 2016. "Bitcoin: a beginning of a new phase?," Economics Bulletin, AccessEcon, vol. 36(3), pages 1430-1440.
    32. repec:dau:papers:123456789/10571 is not listed on IDEAS
    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.
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