Abstract
In this paper, we investigate the co-dependence and portfolio value-at-risk of cryptocurrencies, with the Bitcoin, Ethereum, Litecoin and Ripple price series from January 2016 to December 2021, covering the crypto crash and pandemic period, using the generalized autoregressive score (GAS) model. We find evidence of strong dependence among the virtual currencies with a dynamic structure. The empirical analysis shows that the GAS model smoothly handles volatility and correlation changes, especially during more volatile periods in the markets. We perform a comprehensive comparison of out-of-sample probabilistic forecasts for a range of financial assets and backtests and the GAS model outperforms the classic DCC (dynamic conditional correlation) GARCH model and provides new insights into multivariate risk measures.