The analysis of cryptocurrencies market behaviour is receiving significant attention from researchers and practitioners in the last decades. This paper aims at contributes to volatility estimations of the cryptocurrencies helping to highlight the main stylized facts and characteristics. The performance of different specifications of volatility modelling, within the GARCH class, have been compared through the Model Confidence Set (MCS) over four of the most capitalised cryptocurrencies, namely Bitcoin, Ethereum, Stellar and Ripple. Our empirical findings give evidence of strong asymmetric effects in cryptocurrencies volatility leading to a better performance of asymmetric GARCH specifications..