Using High-Frequency Entropy to Forecast Bitcoin's Daily Value at Risk

In this paper we investigate the ability of several econometrical models to forecast value at risk for a sample of daily time series of cryptocurrency returns. Using high frequency data for Bitcoin, we estimate the entropy of intraday distribution of logreturns through the symbolic time series analysis (STSA), producing low-resolution data from high-resolution data. Our results show that entropy has a strong explanatory power for the quantiles of the distribution of the daily returns. Based on Christoffersen's tests for Value at Risk (VaR) backtesting, we can conclude that the VaR forecast build upon the entropy of intraday returns is the best, compared to the forecasts provided by the classical GARCH models.