Abstract
This paper studies the behaviour of crypto currencies financial time-series of which Bitcoin is the most prominent example. The dynamic of those series is quite complex displaying extreme observations, asymmetries, and several nonlinear characteristics which are difficult to model. We develop a new dynamic model able to account for long-memory and asymmetries in the volatility process as well as for the presence of time-varying skewness and kurtosis. The empirical application, carried out on 606 crypto currencies, indicates that a robust filter for the volatility of crypto currencies is strongly required. Forecasting results show that the inclusion of time{varying skewness systematically improves volatility, density, and quantile predictions at different horizons. Going forward, as this new and unexplored market will develop, our results will be important for asset allocation, risk management, and pricing of derivative securities.
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