  We study the prices of European Emission Allowances (EUA), whereby we analyze
their uncertainty and dependencies on related energy prices (natural gas, coal,
and oil). We propose a probabilistic multivariate conditional time series model
with a VECM-Copula-GARCH structure which exploits key characteristics of the
data. Data are normalized with respect to inflation and carbon emissions to
allow for proper cross-series evaluation. The forecasting performance is
evaluated in an extensive rolling-window forecasting study, covering eight
years out-of-sample. We discuss our findings for both levels- and
log-transformed data, focusing on time-varying correlations, and in view of the
Russian invasion of Ukraine.
