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Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

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  • Aviral Kumar Tiwari
  • Satish Kumar
  • Rajesh Pathak

Abstract

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.

Suggested Citation

  • Aviral Kumar Tiwari & Satish Kumar & Rajesh Pathak, 2019. "Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models," Applied Economics, Taylor & Francis Journals, vol. 51(37), pages 4073-4082, August.
    • Handle: RePEc:taf:applec:v:51:y:2019:i:37:p:4073-4082
    DOI: 10.1080/00036846.2019.1588951
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    Cited by:

    1. Garcia-Jorcano, Laura & Benito, Sonia, 2020. "Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying," Research in International Business and Finance, Elsevier, vol. 54(C).
    2. Almeida, Thiago Ramos, 2024. "Estimating time-varying factors’ variance in the string-term structure model with stochastic volatility," Research in International Business and Finance, Elsevier, vol. 70(PA).
    3. Parthajit Kayal & G. Balasubramanian, 2021. "Excess Volatility in Bitcoin: Extreme Value Volatility Estimation," IIM Kozhikode Society & Management Review, , vol. 10(2), pages 222-231, July.
    4. Będowska-Sójka, Barbara & Kliber, Agata, 2021. "Is there one safe-haven for various turbulences? The evidence from gold, Bitcoin and Ether," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    5. Shi, Yongjing & Tiwari, Aviral Kumar & Gozgor, Giray & Lu, Zhou, 2020. "Correlations among cryptocurrencies: Evidence from multivariate factor stochastic volatility model," Research in International Business and Finance, Elsevier, vol. 53(C).
    6. Alexander, Carol & Deng, Jun & Feng, Jianfen & Wan, Huning, 2023. "Net buying pressure and the information in bitcoin option trades," Journal of Financial Markets, Elsevier, vol. 63(C).
    7. ORĂȘTEAN Ramona & MĂRGINEAN Silvia Cristina & SAVA Raluca, 2019. "Bitcoin In The Scientific Literature – A Bibliometric Study," Studies in Business and Economics, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 14(3), pages 160-174, December.
    8. Yutaka Kurihara & Akio Fukushima & Shinichiro Maeda, 2020. "Can Bitcoin’S Price Be A Predictor Of Stock Prices?," Noble International Journal of Economics and Financial Research, Noble Academic Publsiher, vol. 5(4), pages 50-55, April.
    9. López-Martín, Carmen & Arguedas-Sanz, Raquel & Muela, Sonia Benito, 2022. "A cryptocurrency empirical study focused on evaluating their distribution functions," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 387-407.
    10. Ji Ho Kwon, 2021. "On the factors of Bitcoin’s value at risk," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-31, December.
    11. Jiqian Wang & Feng Ma & Elie Bouri & Yangli Guo, 2023. "Which factors drive Bitcoin volatility: Macroeconomic, technical, or both?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(4), pages 970-988, July.
    12. Pho, Kim Hung & Ly, Sel & Lu, Richard & Hoang, Thi Hong Van & Wong, Wing-Keung, 2021. "Is Bitcoin a better portfolio diversifier than gold? A copula and sectoral analysis for China," International Review of Financial Analysis, Elsevier, vol. 74(C).
    13. Wang, Nianling & Lou, Zhusheng, 2023. "Sequential Bayesian analysis for semiparametric stochastic volatility model with applications," Economic Modelling, Elsevier, vol. 123(C).
    14. Kwon, Ji Ho, 2020. "Tail behavior of Bitcoin, the dollar, gold and the stock market index," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 67(C).
    15. Noriyuki Kunimoto & Kazuhiko Kakamu, 2021. "Is Bitcoin really a currency? A viewpoint of a stochastic volatility model," Papers 2111.15351, arXiv.org.

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