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Dualism in Bitcoin Dynamics: existence of an Upper Bound in Poincaré Recurrence Theorem for Deterministic vs Stochastic Behavior

Author

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  • Grilli, Luca
  • Santoro, Domenico

Abstract

In this paper we want to describe a model of the dynamics of the Bitcoin cryptocurrency system. We can define a duality in these dynamics: Bitcoin mostly behaves as a deterministic system and in some time intervals, much shorter, it enters a stochastic regime. In particular, using Poincaré’s recurrence theorem, it was possible to study when the transition from one regime to another occurs. Furthermore, by applying our hypothesis to real data it was possible to explain a reason why the Bitcoin system is affected by such a "high volatility".

Suggested Citation

  • Grilli, Luca & Santoro, Domenico, 2020. "Dualism in Bitcoin Dynamics: existence of an Upper Bound in Poincaré Recurrence Theorem for Deterministic vs Stochastic Behavior," MPRA Paper 101057, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:101057
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    References listed on IDEAS

    as
    1. Day, Richard H. & Shafer, Wayne, 1987. "Ergodic fluctuations in deterministic economic models," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 339-361, September.
    2. Grilli, Luca & Santoro, Domenico, 2020. "Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach," MPRA Paper 99591, University Library of Munich, Germany.
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    More about this item

    Keywords

    Ergodic Theory; Bitcoin; Finance; Deterministic; Stochastic;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • F17 - International Economics - - Trade - - - Trade Forecasting and Simulation
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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