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Chaos and Order in the Bitcoin Market

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  • Josselin Garnier
  • Knut Solna

Abstract

The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that the bitcoin price exhibits a very interesting multi-scale correlation structure. This structure can be described by a power-law behavior of the variances of the returns as functions of time increments and it can be characterized by two parameters, the volatility and the Hurst exponent. These power-law parameters, however, vary in time. A new notion of generalized Hurst exponent is introduced which allows us to check if the multi-fractal character of the underlying signal is well captured. It is moreover shown how the monitoring of the power-law parameters can be used to identify regime shifts for the bitcoin price. A novel technique for identifying the regimes switches based on a goodness of fit of the local power-law parameters is presented. It automatically detects dates associated with some known events in the bitcoin market place. A very surprising result is moreover that, despite the wild ride of the bitcoin price in recent years and its multi-fractal and non-stationary character, this price has both local power-law behaviors and a very orderly correlation structure when it is observed on its entire period of existence.

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  • Josselin Garnier & Knut Solna, 2018. "Chaos and Order in the Bitcoin Market," Papers 1809.08403, arXiv.org, revised Apr 2019.
    • Handle: RePEc:arx:papers:1809.08403
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    References listed on IDEAS

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    4. Omane-Adjepong, Maurice & Alagidede, Imhotep Paul, 2020. "High- and low-level chaos in the time and frequency market returns of leading cryptocurrencies and emerging assets," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    5. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    6. Bildirici, Melike E. & Sonustun, Bahri, 2021. "Chaotic behavior in gold, silver, copper and bitcoin prices," Resources Policy, Elsevier, vol. 74(C).
    7. Cristiana Vaz & Rui Pascoal & Helder Sebastião, 2021. "Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis," Mathematics, MDPI, vol. 9(17), pages 1-18, August.

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