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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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    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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