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 a large set of crypto{currencies, shows evidence of long memory and leverage effect that has a substantial contribution in the volatility dynamic. Going forward, as this new and unexplored market will develop, our results will be important for investment and risk management purposes.
 

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