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On generalized bivariate student-t Gegenbauer long memory stochastic volatility models with leverage: Bayesian forecasting of cryptocurrencies with a focus on Bitcoin

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  • Phillip, Andrew
  • Chan, Jennifer
  • Peiris, Shelton

Abstract

A Gegenbauer long memory stochastic volatility model with leverage and a bivariate Student’s t-error distribution to model the innovations of the observation and latent volatility jointly for cryptocurrency time series is presented. This is inspired by the deep rooted characteristics found in cryptocurrencies. Until recently their econometric properties have not been thoroughly investigated. Thus, a rigorous in-sample simulation is conducted to assess the performance of the model with its nested alternatives and study the behavior of many cryptocurrencies and in particular Bitcoin. The data analysis is initiated with a broad scope of 114 cryptocurrencies, then a more detailed understanding of five of the most popular cryptocurrencies and followed up with forecasts focused specifically on Bitcoin (while other forecasts are available as supplementary material). The model parameters are estimated with Bayesian approach using Markov Chain Monte Carlo sampling. In order to implement model selection, the Deviance Information Criterion (DIC) is used. Proposed models are compared with many popular models including those commonly used in industry. The models are applied in a Value-at-Risk (VaR) context and several measures are used to assess model performance.

Suggested Citation

  • Phillip, Andrew & Chan, Jennifer & Peiris, Shelton, 2020. "On generalized bivariate student-t Gegenbauer long memory stochastic volatility models with leverage: Bayesian forecasting of cryptocurrencies with a focus on Bitcoin," Econometrics and Statistics, Elsevier, vol. 16(C), pages 69-90.
    • Handle: RePEc:eee:ecosta:v:16:y:2020:i:c:p:69-90
    DOI: 10.1016/j.ecosta.2018.10.003
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    Cited by:

    1. Tak Kuen Siu, 2023. "Bayesian nonlinear expectation for time series modelling and its application to Bitcoin," Empirical Economics, Springer, vol. 64(1), pages 505-537, January.
    2. Constandina Koki & Stefanos Leonardos & Georgios Piliouras, 2019. "A Peek into the Unobservable: Hidden States and Bayesian Inference for the Bitcoin and Ether Price Series," Papers 1909.10957, arXiv.org, revised Jul 2021.
    3. Nitithumbundit, Thanakorn & Chan, Jennifer S.K., 2022. "Covid-19 impact on Cryptocurrencies market using Multivariate Time Series Models," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 365-375.

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    More about this item

    Keywords

    Gegenbauer long memory; Stochastic volatility; Leverage; Heavy tails; Cryptocurrency; Bitcoin;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G1 - Financial Economics - - General Financial Markets

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