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

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  • 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
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    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.

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    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

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