since 08.2024 Professor (full) for Environmental Economics, esp. Economics for Renewable Energies, University of Duisburg-Essen, Germany
03.2023-09.2023 Parental leave (with part time employment as Assistant Professor)
07.2021-10.2021 Parental leave (with part time employment as Assistant Professor)
since 07.2020 Appointed Member of the Junge Akademie at the Berlin-Brandenburg Academy of Sciences and Humanities (BBAW) and the German National Academy of Sciences Leopoldina
02.2017-08.2024 Assistant Professor for Environmental Economics, esp. Economics for Renewable Energies, University of Duisburg-Essen, Germany
04.2019-09.2019 Parental leave (with part time employment as Assistant Professor)
01.2019-04.2019 Visiting researcher in the research programm 'The Mathematics for Energy Systems', Isaac Newton Institute, Cambridge, UK
09.2012-01.2017 Research Associate, Faculty of Business Administration and Economics, European University Viadrina, Frankfurt (Oder), Germany
07.2016-12.2016 Academic Visitor at the Centre for Industrial and Applied Mathematics (OCIAM), University of Oxford, Oxford, UK
09.2012-06.2016 PhD in Business Administration and Economics at the European University Viadrina, Frankfurt (Oder), Germany
06.2015-09.2015 DAAD-visiting research at the European Centre for Advanced Research in Economics and Statistics (ECARES) of the Université libre de Bruxelles (ULB), Brussels, Belgium
10.2008-02.2013 Diplom in Mathematics, Technical University of Dresden, Dresden, Germany
09.2011-08.2012 M.Sc. in Statistics, University College Dublin, Dublin, Ireland
This paper presents a new method for combining (or aggregating or ensembling) multivariate probabilistic forecasts, considering dependencies between quantiles and marginals through a smoothing procedure that allows for online learning. We discuss two smoothing methods: dimensionality reduction using Basis matrices and penalized smoothing. The new online learning algorithm generalizes the standard CRPS learning framework into multivariate dimensions. It is based on Bernstein Online Aggregation (BOA) and yields optimal asymptotic learning properties. The procedure uses horizontal aggregation, i.e., aggregation across quantiles. We provide an in-depth discussion on possible extensions of the algorithm and several nested cases related to the existing literature on online forecast combination. We apply the proposed methodology to forecasting day-ahead electricity prices, which are 24-dimensional distributional forecasts. The proposed method yields significant improvements over uniform combination in terms of continuous ranked probability score (CRPS). We discuss the temporal evolution of the weights and hyperparameters and present the results of reduced versions of the preferred model. A fast C++implementation of the proposed algorithm is provided in the open-source R-Package profoc on CRAN.
Combination and aggregation techniques can significantly improve forecast accuracy. This also holds for probabilistic forecasting methods where predictive distributions are combined. There are several time-varying and adaptive weighting schemes such as Bayesian model averaging (BMA). However, the quality of different forecasts may vary not only over time but also within the distribution. For example, some distribution forecasts may be more accurate in the center of the distributions, while others are better at predicting the tails. Therefore, we introduce a new weighting method that considers the differences in performance over time and within the distribution. We discuss pointwise combination algorithms based on aggregation across quantiles that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of pointwise CRPS learning, we discuss B- and P-Spline-based estimation techniques for batch and online learning, based on quantile regression and prediction with expert advice. We prove that the proposed fully adaptive Bernstein online aggregation (BOA) method for pointwise CRPS online learning has optimal convergence properties. They are confirmed in simulations and a probabilistic forecasting study for European emission allowance (EUA) prices.