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@ARTICLE{Cramer:917556,
      author       = {Cramer, Eike and Witthaut, Dirk and Mitsos, Alexander and
                      Dahmen, Manuel},
      title        = {{M}ultivariate {P}robabilistic {F}orecasting of {I}ntraday
                      {E}lectricity {P}rices using {N}ormalizing {F}lows},
      publisher    = {arXiv},
      reportid     = {FZJ-2023-00758},
      year         = {2022},
      abstract     = {Electricity is traded on various markets with different
                      time horizons and regulations. Short-term intraday trading
                      becomes increasingly important due to the higher penetration
                      of renewables. In Germany, the intraday electricity price
                      typically fluctuates around the day-ahead price of the EPEX
                      spot markets in a distinct hourly pattern. This work
                      proposes a probabilistic modeling approach that models the
                      intraday price difference to the day-ahead contracts. The
                      model captures the emerging hourly pattern by considering
                      the four 15min intervals in each day-ahead price interval as
                      a four-dimensional joint probability distribution. The
                      resulting nontrivial, multivariate price difference
                      distribution is learned using a normalizing flow, i.e., a
                      deep generative model that combines conditional multivariate
                      density estimation and probabilistic regression.
                      Furthermore, this work discusses the influence of different
                      external impact factors based on literature insights and
                      impact analysis using explainable artificial intelligence
                      (XAI). The normalizing flow is compared to an informed
                      selection of historical data and probabilistic forecasts
                      using a Gaussian copula and a Gaussian regression model.
                      Among the different models, the normalizing flow identifies
                      the trends with the highest accuracy and has the narrowest
                      prediction intervals. Both the XAI analysis and the
                      empirical experiments highlight that the immediate history
                      of the price difference realization and the increments of
                      the day-ahead price have the most substantial impact on the
                      price difference.},
      keywords     = {Machine Learning (cs.LG) (Other) / FOS: Computer and
                      information sciences (Other)},
      cin          = {IEK-10},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {1121 - Digitalization and Systems Technology for
                      Flexibility Solutions (POF4-112) / HDS LEE - Helmholtz
                      School for Data Science in Life, Earth and Energy (HDS LEE)
                      (HDS-LEE-20190612)},
      pid          = {G:(DE-HGF)POF4-1121 / G:(DE-Juel1)HDS-LEE-20190612},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2205.13826},
      url          = {https://juser.fz-juelich.de/record/917556},
}