Modeling Volatility and Dependence of European Carbon and Energy Prices

We study the prices of European Emission Allowances (EUA), whereby we analyze their uncertainty and dependencies on related energy markets. We propose a probabilistic multivariate conditional time series model that exploits key characteristics of the data. The forecasting performance of the proposed model and various competing models is evaluated in an extensive rolling window forecasting study, covering almost two years out-of-sample. Thereby, we forecast 30-steps ahead. The accuracy of the multivariate probabilistic forecasts is assessed by the energy score. We discuss our findings focusing on volatility spillovers and time-varying correlations, also in view of the Russian invasion of Ukraine.