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

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  • Fulvia Pennoni
  • Francesco Bartolucci
  • Gianfranco Forte
  • Ferdinando Ametrano

Abstract

A hidden Markov model is proposed for the analysis of time‐series of daily log‐returns of the last 4 years of Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. These log‐returns are assumed to have a multivariate Gaussian distribution conditionally on a latent Markov process having a finite number of regimes or states. The hidden regimes represent different market phases identified through distinct vectors of expected values and variance–covariance matrices of the log‐returns, so that they also differ in terms of volatility. Maximum‐likelihood estimation of the model parameters is carried out by the expectation–maximisation algorithm, and regimes are singularly predicted for every time occasion according to the maximum‐a‐posteriori rule. Results show three positive and three negative phases of the market. In the most recent period, an increasing tendency towards positive regimes is also predicted. A rather heterogeneous correlation structure is estimated, and evidence of structural medium term trend in the correlation of Bitcoin with the other cryptocurrencies is detected.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:ecnote:v:51:y:2022:i:1:n:e12193
    DOI: 10.1111/ecno.12193
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    1. 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.
    2. 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.
    3. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    4. Trimborn, Simon & Härdle, Wolfgang Karl, 2018. "CRIX an Index for cryptocurrencies," Journal of Empirical Finance, Elsevier, vol. 49(C), pages 107-122.
    5. 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.
    6. 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.
    7. Nadarajah, Saralees & Chu, Jeffrey, 2017. "On the inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 150(C), pages 6-9.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Lin, Yu & Xiao, Yang & Li, Fuxing, 2020. "Forecasting crude oil price volatility via a HM-EGARCH model," Energy Economics, Elsevier, vol. 87(C).
    17. Paolo Giudici & Paolo Pagnottoni, 2019. "High Frequency Price Change Spillovers in Bitcoin Markets," Risks, MDPI, vol. 7(4), pages 1-18, November.
    18. 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).
    19. 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.
    20. Fahad Almudhaf, 2018. "Pricing efficiency of Bitcoin Trusts," Applied Economics Letters, Taylor & Francis Journals, vol. 25(7), pages 504-508, April.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. Stephen Chan & Jeffrey Chu & Saralees Nadarajah & Joerg Osterrieder, 2017. "A Statistical Analysis of Cryptocurrencies," JRFM, MDPI, vol. 10(2), pages 1-23, May.
    26. Ying Chen & Paolo Giudici & Branka Hadji Misheva & Simon Trimborn, 2020. "Lead Behaviour in Bitcoin Markets," Risks, MDPI, vol. 8(1), pages 1-14, January.
    27. 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.
    28. 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.
    29. 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.
    30. 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.
    31. Paolo Giudici & Gloria Polinesi, 2021. "Crypto price discovery through correlation networks," Annals of Operations Research, Springer, vol. 299(1), pages 443-457, April.
    32. 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.
    33. 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.
    34. 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.
    35. 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.
    36. Borri, Nicola, 2019. "Conditional tail-risk in cryptocurrency markets," Journal of Empirical Finance, Elsevier, vol. 50(C), pages 1-19.
    37. 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.
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    2. 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.
    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.

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    More about this item

    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

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