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A Statistical Analysis of Cryptocurrencies


  • Stephen Chan


  • Jeffrey Chu


  • Saralees Nadarajah


  • Joerg Osterrieder



We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versus the U.S. Dollar by fitting parametric distributions to them. It is shown that returns are clearly non-normal, however, no single distribution fits well jointly to all the cryptocurrencies analysed. We find that for the most popular currencies, such as Bitcoin and Litecoin, the generalized hyperbolic distribution gives the best fit, while for the smaller cryptocurrencies the normal inverse Gaussian distribution, generalized t distribution, and Laplace distribution give good fits. The results are important for investment and risk management purposes.

Suggested Citation

  • Stephen Chan & Jeffrey Chu & Saralees Nadarajah & Joerg Osterrieder, 2017. "A Statistical Analysis of Cryptocurrencies," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(2), pages 1-23, May.
  • Handle: RePEc:gam:jjrfmx:v:10:y:2017:i:2:p:12-:d:100126

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    References listed on IDEAS

    1. Gabriel Bruneau & Kevin Moran, 2017. "Exchange rate fluctuations and labour market adjustments in Canadian manufacturing industries," Canadian Journal of Economics, Canadian Economics Association, vol. 50(1), pages 72-93, February.
    2. Canan G. Corlu & Alper Corlu, 2015. "Modelling exchange rate returns: which flexible distribution to use?," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1851-1864, November.
    3. Fabio Parlapiano & Vitali Alexeev & Mardi Dungey, 2017. "Exchange rate risk exposure and the value of European firms," The European Journal of Finance, Taylor & Francis Journals, vol. 23(2), pages 111-129, January.
    4. Marie Briere & Kim Oosterlinck & Ariane Szafarz, 2015. "Virtual Currency, Tangible Return: Portfolio Diversification with Bitcoins," Post-Print CEB, ULB -- Universite Libre de Bruxelles, vol. 16(6), pages 365-373.
    5. Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
    6. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    7. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    8. Marcel Schröder, 2017. "The equilibrium real exchange rate and macroeconomic performance in developing countries," Applied Economics Letters, Taylor & Francis Journals, vol. 24(7), pages 506-509, April.
    9. Linden, Mikael, 2001. "A Model for Stock Return Distribution," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 6(2), pages 159-169, April.
    10. Seyyedsajjad Seyyedi, 2017. "Analysis of the Interactive Linkages Between Gold Prices, Oil Prices, and Exchange Rate in India," Global Economic Review, Taylor & Francis Journals, vol. 46(1), pages 65-79, January.
    11. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    12. Zhiguo He & Arvind Krishnamurthy, 2012. "A macroeconomic framework for quantifying systemic risk," Working Paper Research 233, National Bank of Belgium.
    13. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    14. Harald Kinateder, 2015. "What drives tail risk in aggregate European equity markets?," Journal of Risk Finance, Emerald Group Publishing, vol. 16(4), pages 395-406, August.
    15. Saralees Nadarajah & Emmanuel Afuecheta & Stephen Chan, 2015. "A note on "Modelling exchange rate returns: which flexible distribution to use?"," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1777-1785, November.
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    Cited by:

    1. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Nonextensive triplets in cryptocurrency exchanges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1069-1074.
    2. Omane-Adjepong, Maurice & Alagidede, Paul & Akosah, Nana Kwame, 2019. "Wavelet time-scale persistence analysis of cryptocurrency market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 105-120.
    3. Eduard Silantyev, 2019. "Order flow analysis of cryptocurrency markets," Digital Finance, Springer, vol. 1(1), pages 191-218, November.
    4. White, Reilly & Marinakis, Yorgos & Islam, Nazrul & Walsh, Steven, 2020. "Is Bitcoin a currency, a technology-based product, or something else?," Technological Forecasting and Social Change, Elsevier, vol. 151(C).
    5. Yuan Hu & Svetlozar T. Rache & Frank J. Fabozzi, 2019. "Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option Valuation," Papers 1908.05419,
    6. Zhang, Yuanyuan & Chan, Stephen & Chu, Jeffrey & Nadarajah, Saralees, 2019. "Stylised facts for high frequency cryptocurrency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 598-612.
    7. Marian Gidea & Daniel Goldsmith & Yuri Katz & Pablo Roldan & Yonah Shmalo, 2018. "Topological recognition of critical transitions in time series of cryptocurrencies," Papers 1809.00695,
    8. Rodolfo Angelo Magtanggol Iii De Guzman & Mike K. P. So, 2018. "Empirical Analysis Of Bitcoin Prices Using Threshold Time Series Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 1-24, December.
    9. Damian Zięba, 2019. "Lévy processes on the cryptocurrency market," Working Papers 2019-15, Faculty of Economic Sciences, University of Warsaw.
    10. 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).
    11. Dean Fantazzini & Stephan Zimin, 2020. "A multivariate approach for the simultaneous modelling of market risk and credit risk for cryptocurrencies," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 47(1), pages 19-69, March.
    12. Lorenzo Lucchini & Laura Alessandretti & Bruno Lepri & Angela Gallo & Andrea Baronchelli, 2020. "From code to market: Network of developers and correlated returns of cryptocurrencies," Papers 2004.07290,
    13. Gregor Dorfleitner & Carina Lung, 2018. "Cryptocurrencies from the perspective of euro investors: a re-examination of diversification benefits and a new day-of-the-week effect," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 472-494, December.
    14. Liu, Weiyi, 2019. "Portfolio diversification across cryptocurrencies," Finance Research Letters, Elsevier, vol. 29(C), pages 200-205.
    15. Gidea, Marian & Goldsmith, Daniel & Katz, Yuri & Roldan, Pablo & Shmalo, Yonah, 2020. "Topological recognition of critical transitions in time series of cryptocurrencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    16. Nils Bundi & Marc Wildi, 2019. "Bitcoin and market-(in)efficiency: a systematic time series approach," Digital Finance, Springer, vol. 1(1), pages 47-65, November.
    17. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    18. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2019. "Exploring disorder and complexity in the cryptocurrency space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 548-556.
    19. Anastasiadis Panagiotis & Katsaros Efthymios & Koutsioukis Anastasios-Taxiarchis & Pandazis Athanasios, 2020. "GARCH Modelling of High-Capitalization Cryptocurrencies' Impacts During Bearish Markets," Journal of Central Banking Theory and Practice, Central bank of Montenegro, vol. 9(3), pages 87-106.
    20. Liu, Weiyi & Liang, Xuan & Cui, Guowei, 2020. "Common risk factors in the returns on cryptocurrencies," Economic Modelling, Elsevier, vol. 86(C), pages 299-305.
    21. Chu, Jeffrey & Zhang, Yuanyuan & Chan, Stephen, 2019. "The adaptive market hypothesis in the high frequency cryptocurrency market," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 221-231.
    22. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2019. "Multifractal behavior of price and volume changes in the cryptocurrency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 54-61.
    23. Chu, Jeffrey & Chan, Stephen & Zhang, Yuanyuan, 2020. "High frequency momentum trading with cryptocurrencies," Research in International Business and Finance, Elsevier, vol. 52(C).

    More about this item


    exchange rate; distributions; blockchain; Bitcoin;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • E - Macroeconomics and Monetary Economics
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • G - Financial Economics


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