IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/106150.html
   My bibliography  Save this paper

Exploring the dependencies among main cryptocurrency log-returns: A hidden Markov model

Author

Listed:
  • Pennoni, Fulvia
  • Bartolucci, Francesco
  • Forte, Gianfranco
  • Ametrano, Ferdinando

Abstract

A multivariate hidden Markov model is proposed to explain the price evolution of Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. The observed daily log-returns of these five major cryptocurrencies are modeled jointly. They are assumed to be correlated according to a variance-covariance matrix conditionally on a latent Markov process having a finite number of states. For the purpose of comparing states according to their volatility, we estimate specific variance-covariance matrix varying across states. Maximum likelihood estimation of the model parameters is carried out by the Expectation-Maximization algorithm. The hidden states represent different phases of the market identified through the estimated expected values and volatility of the log-returns. We reach interesting results in detecting these phases of the market and the implied transition dynamics. We also find evidence of structural medium term trend in the correlations of Bitcoin with the other cryptocurrencies.

Suggested Citation

  • Pennoni, Fulvia & Bartolucci, Francesco & Forte, Gianfranco & Ametrano, Ferdinando, 2020. "Exploring the dependencies among main cryptocurrency log-returns: A hidden Markov model," MPRA Paper 106150, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:106150
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/106150/1/MPRA_paper_106150.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    2. Sifat, Imtiaz Mohammad & Mohamad, Azhar & Mohamed Shariff, Mohammad Syazwan Bin, 2019. "Lead-Lag relationship between Bitcoin and Ethereum: Evidence from hourly and daily data," Research in International Business and Finance, Elsevier, vol. 50(C), pages 306-321.
    3. Jan Jakub Szczygielski & Andreas Karathanasopoulos & Adam Zaremba, 2020. "One shape fits all? A comprehensive examination of cryptocurrency return distributions," Applied Economics Letters, Taylor & Francis Journals, vol. 27(19), pages 1567-1573, November.
    4. Alvarez-Ramirez, J. & Rodriguez, E. & Ibarra-Valdez, C., 2018. "Long-range correlations and asymmetry in the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 948-955.
    5. Fulvia Pennoni & Francesco Bartolucci & Gianfranco Forte & Ferdinando Ametrano, 2022. "Exploring the dependencies among main cryptocurrency log‐returns: A hidden Markov model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(1), February.
    6. Sha Wang & Jean-Philippe Vergne, 2017. "Buzz Factor or Innovation Potential: What Explains Cryptocurrencies’ Returns?," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-17, January.
    7. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    8. Trimborn, Simon & Härdle, Wolfgang Karl, 2018. "CRIX an Index for cryptocurrencies," Journal of Empirical Finance, Elsevier, vol. 49(C), pages 107-122.
    9. Tiwari, Aviral Kumar & Jana, R.K. & Das, Debojyoti & Roubaud, David, 2018. "Informational efficiency of Bitcoin—An extension," Economics Letters, Elsevier, vol. 163(C), pages 106-109.
    10. Borri, Nicola, 2019. "Conditional tail-risk in cryptocurrency markets," Journal of Empirical Finance, Elsevier, vol. 50(C), pages 1-19.
    11. Luca De Angelis & Leonard J. Paas, 2013. "A dynamic analysis of stock markets using a hidden Markov model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1682-1700, August.
    12. Bariviera, Aurelio F. & Basgall, María José & Hasperué, Waldo & Naiouf, Marcelo, 2017. "Some stylized facts of the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 82-90.
    13. Langrock, Roland & MacDonald, Iain L. & Zucchini, Walter, 2012. "Some nonstandard stochastic volatility models and their estimation using structured hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 19(1), pages 147-161.
    14. Wei Zhang & Pengfei Wang & Xiao Li & Dehua Shen, 2018. "Some stylized facts of the cryptocurrency market," Applied Economics, Taylor & Francis Journals, vol. 50(55), pages 5950-5965, November.
    15. Nadarajah, Saralees & Chu, Jeffrey, 2017. "On the inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 150(C), pages 6-9.
    16. Ying Chen & Paolo Giudici & Branka Hadji Misheva & Simon Trimborn, 2020. "Lead Behaviour in Bitcoin Markets," Risks, MDPI, vol. 8(1), pages 1-14, January.
    17. Cheah, Eng-Tuck & Fry, John, 2015. "Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin," Economics Letters, Elsevier, vol. 130(C), pages 32-36.
    18. Bartolucci, F. & De Luca, G., 2003. "Likelihood-based inference for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 445-449, March.
    19. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "High frequency volatility co-movements in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 62(C), pages 35-52.
    20. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    21. Yi, Shuyue & Xu, Zishuang & Wang, Gang-Jin, 2018. "Volatility connectedness in the cryptocurrency market: Is Bitcoin a dominant cryptocurrency?," International Review of Financial Analysis, Elsevier, vol. 60(C), pages 98-114.
    22. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    23. Nasri, Bouchra R. & Rémillard, Bruno N., 2019. "Copula-based dynamic models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 107-121.
    24. Xiong, Jinwu & Liu, Qing & Zhao, Lei, 2020. "A new method to verify Bitcoin bubbles: Based on the production cost," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    25. Bouri, Elie & Shahzad, Syed Jawad Hussain & Roubaud, David, 2019. "Co-explosivity in the cryptocurrency market," Finance Research Letters, Elsevier, vol. 29(C), pages 178-183.
    26. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    27. Corbet, Shaen & Meegan, Andrew & Larkin, Charles & Lucey, Brian & Yarovaya, Larisa, 2018. "Exploring the dynamic relationships between cryptocurrencies and other financial assets," Economics Letters, Elsevier, vol. 165(C), pages 28-34.
    28. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
    29. Arianna Agosto & Alessia Cafferata, 2020. "Financial Bubbles: A Study of Co-Explosivity in the Cryptocurrency Market," Risks, MDPI, vol. 8(2), pages 1-14, April.
    30. Fahad Almudhaf, 2018. "Pricing efficiency of Bitcoin Trusts," Applied Economics Letters, Taylor & Francis Journals, vol. 25(7), pages 504-508, April.
    31. Paolo Giudici & Paolo Pagnottoni, 2020. "Vector error correction models to measure connectedness of Bitcoin exchange markets," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(1), pages 95-109, January.
    32. Paolo Giudici & Gloria Polinesi, 2021. "Crypto price discovery through correlation networks," Annals of Operations Research, Springer, vol. 299(1), pages 443-457, April.
    33. Stephen Chan & Jeffrey Chu & Saralees Nadarajah & Joerg Osterrieder, 2017. "A Statistical Analysis of Cryptocurrencies," JRFM, MDPI, vol. 10(2), pages 1-23, May.
    34. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1043-1078, November.
    35. Lin, Yu & Xiao, Yang & Li, Fuxing, 2020. "Forecasting crude oil price volatility via a HM-EGARCH model," Energy Economics, Elsevier, vol. 87(C).
    36. Paolo Giudici & Paolo Pagnottoni, 2019. "High Frequency Price Change Spillovers in Bitcoin Markets," Risks, MDPI, vol. 7(4), pages 1-18, November.
    37. Dias, José G. & Vermunt, Jeroen K. & Ramos, Sofia, 2015. "Clustering financial time series: New insights from an extended hidden Markov model," European Journal of Operational Research, Elsevier, vol. 243(3), pages 852-864.
    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. Fulvia Pennoni & Francesco Bartolucci & Gianfranco Forte & Ferdinando Ametrano, 2022. "Exploring the dependencies among main cryptocurrency log‐returns: A hidden Markov model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(1), February.
    2. Mercik, Aleksander & Słoński, Tomasz & Karaś, Marta, 2024. "Understanding crypto-asset exposure: An investigation of its impact on performance and stock sensitivity among listed companies," International Review of Financial Analysis, Elsevier, vol. 92(C).
    3. Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.

    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. Flori, Andrea, 2019. "News and subjective beliefs: A Bayesian approach to Bitcoin investments," Research in International Business and Finance, Elsevier, vol. 50(C), pages 336-356.
    2. De Pace, Pierangelo & Rao, Jayant, 2023. "Comovement and instability in cryptocurrency markets," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 173-200.
    3. Vidal-Tomás, David, 2021. "The entry and exit dynamics of the cryptocurrency market," Research in International Business and Finance, Elsevier, vol. 58(C).
    4. Aurelio F. Bariviera & Ignasi Merediz‐Solà, 2021. "Where Do We Stand In Cryptocurrencies Economic Research? A Survey Based On Hybrid Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 377-407, April.
    5. Andrea Flori, 2019. "Cryptocurrencies In Finance: Review And Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-22, August.
    6. Corbet, Shaen & Lucey, Brian & Urquhart, Andrew & Yarovaya, Larisa, 2019. "Cryptocurrencies as a financial asset: A systematic analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 182-199.
    7. Arianna Agosto & Alessia Cafferata, 2020. "Financial Bubbles: A Study of Co-Explosivity in the Cryptocurrency Market," Risks, MDPI, vol. 8(2), pages 1-14, April.
    8. Almeida, José & Gonçalves, Tiago Cruz, 2023. "A systematic literature review of investor behavior in the cryptocurrency markets," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    9. Li, Mu-Yao & Cai, Qing & Gu, Gao-Feng & Zhou, Wei-Xing, 2019. "Exponentially decayed double power-law distribution of Bitcoin trade sizes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    10. Chen, Bin-xia & Sun, Yan-lin, 2024. "Risk characteristics and connectedness in cryptocurrency markets: New evidence from a non-linear framework," The North American Journal of Economics and Finance, Elsevier, vol. 69(PA).
    11. Costantini, Mauro & Maaitah, Ahmad & Mishra, Tapas & Sousa, Ricardo M., 2023. "Bitcoin market networks and cyberattacks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    12. Abakah, Emmanuel Joel Aikins & Gil-Alana, Luis Alberiko & Madigu, Godfrey & Romero-Rojo, Fatima, 2020. "Volatility persistence in cryptocurrency markets under structural breaks," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 680-691.
    13. Stefano Martinazzi & Daniele Regoli & Andrea Flori, 2020. "A Tale of Two Layers: The Mutual Relationship between Bitcoin and Lightning Network," Risks, MDPI, vol. 8(4), pages 1-18, December.
    14. Omane-Adjepong, Maurice & Alagidede, Paul & Akosah, Nana Kwame, 2019. "Wavelet time-scale persistence analysis of cryptocurrency market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 105-120.
    15. Yaya, OlaOluwa S. & Ogbonna, Ahamuefula E. & Olubusoye, Olusanya E., 2019. "How persistent and dynamic inter-dependent are pricing of Bitcoin to other cryptocurrencies before and after 2017/18 crash?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    16. Helder Miguel Correia Virtuoso Sebastião & Paulo José Osório Rupino Da Cunha & Pedro Manuel Cortesão Godinho, 2021. "Cryptocurrencies and blockchain. Overview and future perspectives," International Journal of Economics and Business Research, Inderscience Enterprises Ltd, vol. 21(3), pages 305-342.
    17. Corbet, Shaen & Larkin, Charles & Lucey, Brian & Meegan, Andrew & Yarovaya, Larisa, 2020. "Cryptocurrency reaction to FOMC Announcements: Evidence of heterogeneity based on blockchain stack position," Journal of Financial Stability, Elsevier, vol. 46(C).
    18. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "The inefficiency of cryptocurrency and its cross-correlation with Dow Jones Industrial Average," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 658-670.
    19. Agosto, Arianna & Cerchiello, Paola & Pagnottoni, Paolo, 2022. "Sentiment, Google queries and explosivity in the cryptocurrency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    20. Bazán-Palomino, Walter, 2022. "Interdependence, contagion and speculative bubbles in cryptocurrency markets," Finance Research Letters, Elsevier, vol. 49(C).

    More about this item

    Keywords

    Bitcoin; Bitcoin cash; decoding; Ethereum; expectation-maximization algorithm; Litecoin; Ripple; time-series;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:106150. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.