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Statistical analysis of bitcoin during explosive behavior periods

Author

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  • José Antonio Núñez
  • Mario I Contreras-Valdez
  • Carlos A Franco-Ruiz

Abstract

This paper develops the ability of the normal inverse Gaussian distribution (NIG) to fit the returns of bitcoin (BTC). As the first cryptocurrency created, the behavior of this new asset is characterized by great volatility. The lack of a proper definition or classification under existing theory exacerbates this property in such a way that explosive periods followed by a rapid decline have been observed along the series, meaning bubble episodes. By detecting the periods in which a bubble rises and collapses, it is possible to study the statistical properties of such segments. In particular, adjusting a theoretical distribution may help to determine better strategies to hedge against these episodes. The NIG is an appropriate candidate not only because of its heavy-tailed property but also because it has been proven to be closed under convolution, a characteristic that can be implemented to measure multivariate value at risk. Using data on the price of BTC with respect to seven of the main global currencies, the NIG was able to fit every time segment despite the bubble behavior. In the out-of-sample tests, the NIG was proven to have an adjustment similar to that of a generalized hyperbolic (GH) distribution. This result could serve as a starting point for future studies regarding the statistical properties of cryptocurrencies as well as their multivariate distributions.

Suggested Citation

  • José Antonio Núñez & Mario I Contreras-Valdez & Carlos A Franco-Ruiz, 2019. "Statistical analysis of bitcoin during explosive behavior periods," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-22, March.
    • Handle: RePEc:plo:pone00:0213919
    DOI: 10.1371/journal.pone.0213919
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    References listed on IDEAS

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    4. Mario I. Contreras-Valdez & José Antonio Núñez & Guillermo Benavides Perales, 2022. "Bitcoin in Portfolio Selection: A Multivariate Distribution Approach," SAGE Open, , vol. 12(2), pages 21582440221, May.
    5. da Cunha, C.R. & da Silva, R., 2020. "Relevant stylized facts about bitcoin: Fluctuations, first return probability, and natural phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    6. 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.
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    8. Wei Sun & Alisher Tohirovich Dedahanov & Ho Young Shin & Ki Su Kim, 2020. "Switching intention to crypto-currency market: Factors predisposing some individuals to risky investment," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-16, June.
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    10. Sun, Wei & Dedahanov, Alisher Tohirovich & Shin, Ho Young & Li, Wei Ping, 2021. "Factors affecting institutional investors to add crypto-currency to asset portfolios," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).

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