Title: Modelling and predicting the Bitcoin volatility using GARCH models

Authors: Viviane Y. Naimy; Marianne R. Hayek

Addresses: Faculty of Business Administration and Economics, Notre Dame University, Louaize, 1211, Lebanon ' Faculty of Business Administration and Economics, Notre Dame University, Louaize, 1211, Lebanon

Abstract: This paper is the first to forecast the volatility of the Bitcoin/USD exchange rate. It assesses and compares the predictive ability of the generalised autoregressive conditional heteroscedasticity (GARCH) (1,1), the exponentially weighted moving average (EWMA), and the exponential generalised autoregressive conditional heteroscedasticity (EGARCH) (1,1). Models' parameters are first estimated from the in sample Bitcoin/USD exchange rate returns and in sample volatility is calculated. Out of sample volatility is forecasted afterward. Estimated volatilities are then compared to realised volatilities relying on error statistics, after which the models are ranked. The EGARCH (1,1) model outperforms the GARCH (1,1) and EWMA models in both in sample and out of sample contexts with increased accuracy in the out of sample period. Results show an original reflection concern with regard to the nature of the Bitcoin, which behaves differently than traditional currencies. Given the early-stage behaviour of the Bitcoin, results might change in the future.

Keywords: Bitcoin; modelling volatility; predictive ability; GARCH(1,1); EWMA; exponentially weighted moving average; EGARCH; exponential generalised autoregressive conditional heteroscedasticity; in sample; out of sample; optimisation; errors test statistics.

DOI: 10.1504/IJMMNO.2018.088994

International Journal of Mathematical Modelling and Numerical Optimisation, 2018 Vol.8 No.3, pp.197 - 215

Available online: 26 Dec 2017 *

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