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Forecasting volatility in bitcoin market

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Abstract

In this paper, we revisit the stylized facts of bitcoin markets and propose various approaches for modeling the dynamics governing the mean and variance processes. We first provide the statistical properties of our proposed models and study in detail their forecasting performance and adequacy by means of point and density forecasts. We adopt two loss functions and the model confidence set test to evaluate the predictive ability of the models and the likelihood ratio test to assess their adequacy. Our results confirm that bitcoin markets are characterized by regime shifting, long memory and multifractality. We find that the Markov switching multifractal and FIGARCH models outperform other GARCH-type models in forecasting bitcoin returns volatility. Furthermore, combined forecasts improve upon forecasts from individual models.

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Notes

  1. Liu et al. (2007) find that assuming other base distributions, such as lognormal and gamma, makes little difference in empirical applications.

  2. We note that the EGARCH process models the logarithm of the variance and enables positivity constraints on the model parameters to be relaxed. However, forecasts of conditional variances from the EGARCH model are the optimal least squares forecasts for logarithm volatility and biased, because by Jensen’s inequality \({{\,\mathrm{\mathbb {E}}\,}}(\sigma ^2_t)\ge \exp [{{\,\mathrm{\mathbb {E}}\,}}(\log \sigma ^2_t)]\).

  3. The parameters \(\psi _i\) in the series expansion can be obtained via the following recursions \(\psi _1 = \phi - \beta + \tau d\) and \(\psi _i = \beta \psi _{i-1} + \left( \frac{i-1-d}{i}-\phi \right) \chi _{d,i-1}\) for \(i=2,\dots ,\infty \) where \(\chi _{d,i} = \chi _{d,i-1}\left( i-1-d\right) /i\) with \(\chi _{d,1}=\tau d\). We impose, however, a finite truncation at lag 1000 in the estimation procedures.

  4. We refer the reader to Pesaran and Timmermann (2007) for more details on selection of an optimal window in the presence of breaks.

  5. Financialisation implies that large changes of the prices and waves of high and low fluctuations might be caused by the trading process and might not necessarily reflect exogenous sources of uncertainty.

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Authors and Affiliations

  1. Department of Economics, Institute for Econometric and Economic Statistics and Empirical Economics, University of Münster, Münster, Germany

    Mawuli Segnon

  2. Department of Economics, European University Institute, Florence, Italy

    Stelios Bekiros

  3. Athens University of Economics & Business, Athens, Greece

    Stelios Bekiros

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  1. Mawuli Segnon
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  2. Stelios Bekiros
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Correspondence to Stelios Bekiros.

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Segnon, M., Bekiros, S. Forecasting volatility in bitcoin market. Ann Finance 16, 435–462 (2020). https://doi.org/10.1007/s10436-020-00368-y

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