IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v638y2024ics0378437124001171.html
   My bibliography  Save this article

A permutation entropy analysis of Bitcoin volatility

Author

Listed:
  • Obanya, Praise Otito
  • Seitshiro, Modisane
  • Olivier, Carel Petrus
  • Verster, Tanja

Abstract

Cryptocurrencies are widely regarded as volatile and less predictable assets by financial participants. The behaviour and dynamics of Bitcoin’s daily volatility, obtained by fitting GARCH models, are investigated for a period of 8 years using permutation entropy which is represented by the variable H for calculations. The best fitting GARCH models selected are the FIGARCH(1,0.7,1) and SGARCH(1,1) models based on maximum likelihood estimation, Akaike Information Criterion and Bayesian Information Criterion. Simulated volatilities are also obtained from the best fitting GARCH models using their respective parameters, to confirm how well the models fit. The results obtained show that the H values of Bitcoin are generally low and that the dynamics of Bitcoin’s volatility is quite predictable, as Bitcoin’s volatility is most likely to decline over time than increase or have an alternating movement. Also, the simulated volatilities show good agreement with the real-world volatility, confirming the models as good fits.

Suggested Citation

  • Obanya, Praise Otito & Seitshiro, Modisane & Olivier, Carel Petrus & Verster, Tanja, 2024. "A permutation entropy analysis of Bitcoin volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    • Handle: RePEc:eee:phsmap:v:638:y:2024:i:c:s0378437124001171
    DOI: 10.1016/j.physa.2024.129609
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437124001171
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2024.129609?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. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. 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.
    3. repec:men:wpaper:58_2015 is not listed on IDEAS
    4. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    5. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    7. Heather Mitchell & Michael Mckenzie, 2003. "GARCH model selection criteria," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 262-284.
    8. Siokis, Fotios M., 2018. "Credit market Jitters in the course of the financial crisis: A permutation entropy approach in measuring informational efficiency in financial assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 266-275.
    9. Zhenghui Li & Hao Dong & Christos Floros & Athanasios Charemis & Pierre Failler, 2022. "Re-examining Bitcoin Volatility: A CAViaR-based Approach," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 58(5), pages 1320-1338, April.
    10. 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.
    11. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.
    12. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    13. 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.
    14. Jaroslav Bukovina & Matus Marticek, 2016. "Sentiment and Bitcoin Volatility," MENDELU Working Papers in Business and Economics 2016-58, Mendel University in Brno, Faculty of Business and Economics.
    15. Balcilar, Mehmet & Bouri, Elie & Gupta, Rangan & Roubaud, David, 2017. "Can volume predict Bitcoin returns and volatility? A quantiles-based approach," Economic Modelling, Elsevier, vol. 64(C), pages 74-81.
    16. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    17. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    18. Dias, Ishanka K. & Fernando, J.M. Ruwani & Fernando, P. Narada D., 2022. "Does investor sentiment predict bitcoin return and volatility? A quantile regression approach," International Review of Financial Analysis, Elsevier, vol. 84(C).
    19. Cina Aghamohammadi & Mehran Ebrahimian & Hamed Tahmooresi, 2014. "Permutation approach, high frequency trading and variety of micro patterns in financial time series," Papers 1407.5254, arXiv.org.
    20. 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.
    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. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    2. Brooks, Robert D. & Faff, Robert W. & McKenzie, Michael D. & Mitchell, Heather, 2000. "A multi-country study of power ARCH models and national stock market returns," Journal of International Money and Finance, Elsevier, vol. 19(3), pages 377-397, June.
    3. Siwen Zhou, 2021. "Exploring the driving forces of the Bitcoin currency exchange rate dynamics: an EGARCH approach," Empirical Economics, Springer, vol. 60(2), pages 557-606, February.
    4. Vacca, Gianmarco & Zoia, Maria Grazia & Bagnato, Luca, 2022. "Forecasting in GARCH models with polynomially modified innovations," International Journal of Forecasting, Elsevier, vol. 38(1), pages 117-141.
    5. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    6. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    7. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    8. Conrad, Christian & Karanasos, Menelaos & Zeng, Ning, 2011. "Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 147-159, January.
    9. Köksal, Bülent, 2009. "A Comparison of Conditional Volatility Estimators for the ISE National 100 Index Returns," MPRA Paper 30510, University Library of Munich, Germany.
    10. repec:awi:wpaper:0472 is not listed on IDEAS
    11. Stelios Arvanitis & Antonis Demos, 2004. "Time Dependence and Moments of a Family of Time‐Varying Parameter Garch in Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 1-25, January.
    12. Mauro Bernardi & Leopoldo Catania, 2016. "Comparison of Value-at-Risk models using the MCS approach," Computational Statistics, Springer, vol. 31(2), pages 579-608, June.
    13. Trino-Manuel Ñíguez, 2003. "Volatility And Var Forecasting For The Ibex-35 Stock-Return Index Using Figarch-Type Processes And Different Evaluation Criteria," Working Papers. Serie AD 2003-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    14. Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," JRFM, MDPI, vol. 10(4), pages 1-15, October.
    15. Milton Abdul Thorlie & Lixin Song & Muhammad Amin & Xiaoguang Wang, 2015. "Modeling and forecasting of stock index volatility with APARCH models under ordered restriction," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 329-356, August.
    16. 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).
    17. S. M. Abdullah & Salina Siddiqua & Muhammad Shahadat Hossain Siddiquee & Nazmul Hossain, 2017. "Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models: a comparison based on normal and Student’s t-error distribution," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 3(1), pages 1-19, December.
    18. Michael McKenzie & Heather Mitchell & Robert Brooks & Robert Faff, 2001. "Power ARCH modelling of commodity futures data on the London Metal Exchange," The European Journal of Finance, Taylor & Francis Journals, vol. 7(1), pages 22-38.
    19. Y. K. Tse, 2002. "Residual-based diagnostics for conditional heteroscedasticity models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 358-374, June.
    20. Carnero, María Ángeles & Peña, Daniel & Ruiz Ortega, Esther, 2001. "Outliers and conditional autoregressive heteroscedasticity in time series," DES - Working Papers. Statistics and Econometrics. WS ws010704, Universidad Carlos III de Madrid. Departamento de Estadística.
    21. Geoffrey F. Loudon & Wing H. Watt & Pradeep K. Yadav, 2000. "An empirical analysis of alternative parametric ARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 117-136.

    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:eee:phsmap:v:638:y:2024:i:c:s0378437124001171. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.