  Combination and aggregation techniques can improve forecast accuracy
substantially. This also holds for probabilistic forecasting methods where full
predictive distributions are combined. There are several time-varying and
adaptive weighting schemes like Bayesian model averaging (BMA). However, the
performance of different forecasters may vary not only over time but also in
parts of the distribution. So one may be more accurate in the center of the
distributions, and other ones perform better in predicting the distribution's
tails. Consequently, we introduce a new weighting procedure that considers both
varying performance across time and the distribution. We discuss pointwise
online aggregation algorithms that optimize with respect to the continuous
ranked probability score (CRPS). After analyzing the theoretical properties of
a fully adaptive Bernstein online aggregation (BOA) method, we introduce
smoothing procedures for pointwise CRPS learning. The properties are confirmed
and discussed using simulation studies. Additionally, we illustrate the
performance in a forecasting study for carbon markets. In detail, we predict
the distribution of European emission allowance prices.
