Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Modelling the volatility of Bitcoin returns using GARCH models

Department of Mathematics, Pan African University, Institute for Basic Sciences, Technology, and Innovation, Kenya

Bitcoin has received a lot of attention from both investors and analysts, as it forms the highest market capitalization in the cryptocurrency market. This paper evaluates the volatility of Bitcoin returns using three GARCH models (sGARCH, iGARCH, and tGARCH). The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skewed distribution in the return series of Bitcoin. Comparative to the Students’t-distribution and the Generalized error distribution, the Normal Inverse Gaussian (NIG) distribution captured adequately the leptokurtic and skewness in all the GARCH models. The tGARCH model was the best model as it described the asymmetric occurrence of shocks in the Bitcoin market. That is, the response of investors to the same amount of good and bad news are distinct. From the empirical results, it can be concluded that tGARCH-NIG was the best model to estimate the volatility in the return series of Bitcoin. Generally, it would be optimal to use the NIG distribution in GARCH type models since time series of most cryptocurrency are leptokurtic.
  Article Metrics

Keywords cryptocurrency; Bitcoin; volatility; tGARCH; Normal Inverse Gaussian

Citation: Samuel Asante Gyamerah. Modelling the volatility of Bitcoin returns using GARCH models. Quantitative Finance and Economics, 2019, 3(4): 739-753. doi: 10.3934/QFE.2019.4.739


  • 1. Anderson TW, Darling DA(1954) A test of goodness of fit. J Am Stat Assoc 49: 765-769.
  • 2. Barndorff-Nielsen O (1977) Exponentially decreasing distributions for the logarithm of particle size. Proc Royal Society London A Math Phys Sci 353: 401-419.    
  • 3. Bollerslev T(1986) Generalized autoregressive conditional heteroskedasticity. J Econometrics 31: 307-327.
  • 4. Bouri E, Azzi G, Dyhrberg AH (2013) On the return-volatility relationship in the bitcoin market around the price crash of 2013. Available at SSRN 2869855.
  • 5. Box GE, Pierce DA(1970) Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. J Am Stat Assoc 65: 1509-1526.
  • 6. Chu J, Chan S, Nadarajah S, et al. (2017) Garch modelling of cryptocurrencies. J Risk Financ Manage 10: 17.    
  • 7. Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root, J Am Stat Assoc 74: 427-431.
  • 8. Dyhrberg AH (2016) Hedging capabilities of bitcoin. is it the virtual gold? Financ Res Lett 16: 139-144.
  • 9. Engle R (2001) Garch 101: The use of arch/garch models in applied econometrics. J Econ Perspect 15: 157-168.    
  • 10. Gronwald M (2014) The economics of bitcoins-market characteristics and price jumps.
  • 11. Glosten LR, Jagannathan R, Runkle DE (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. J Financ 48:1779-1801.    
  • 12. Jarque CM, Bera AK(1987) A test for normality of observations and regression residuals. Int Stat Rev/Revue Internationale de Statistique, 163-172.
  • 13. Katsiampa P (2017) Volatility estimation for bitcoin: A comparison of garch models. Econ Lett 158: 3-6.    
  • 14. Ravichandran K, Bose S, Akgiray V, et al. (1989) Threshold generalized autoregressive conditional heteroskedasticity models. Res J Bus Manage 6: 55-80.
  • 15. Student (1908) The probable error of a mean. Biometrika, 1-25.


This article has been cited by

  • 1. Pierre J. Venter, Eben Maré, GARCH Generated Volatility Indices of Bitcoin and CRIX, Journal of Risk and Financial Management, 2020, 13, 6, 121, 10.3390/jrfm13060121
  • 2. Zhenghui Li, Yan Wang, Zhehao Huang, Risk Connectedness Heterogeneity in the Cryptocurrency Markets, Frontiers in Physics, 2020, 8, 10.3389/fphy.2020.00243
  • 3. Mohammad Reza Abbaszadeh, Mehdi Jabbari Nooghabi, Mohammad Mahdi Rounaghi, Using Lyapunov’s method for analysing of chaotic behaviour on financial time series data: a case study on Tehran stock exchange, National Accounting Review, 2020, 2, 3, 297, 10.3934/NAR.2020017

Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved