The forecasting literature on intraday electricity markets is scarce and restricted to the analysis of volume-weighted average prices. These only admit a highly aggregated representation of the market. Instead, we propose to forecast the entire volume-weighted price distribution. We approximate this distribution in a non-parametric way using a dense grid of quantiles. We conduct a forecasting study on data from the German intraday market and aim to forecast the quantiles for the last three hours before delivery. We compare the performance of several linear regression models and an ensemble of neural networks to several well designed naive benchmarks. The forecasts only improve marginally over the naive benchmarks for the central quantiles of the distribution which is in line with the latest empirical results in the literature. However, we are able to significantly outperform all benchmarks for the tails of the price distribution.

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<p>Statistical post-processing of ensemble forecasts has become a common practice in research to correct biases and errors in calibration. While many of the developments have been focused on univariate methods that calibrate the marginal distributions, practical applications often require accurate modeling of spatial, temporal, and inter-variable dependencies. Copula-based multivariate post-processing methods, such as ensemble copula coupling, have been proposed to address this issue and proceed by reordering univariately post-processed ensembles with copula functions to retain the dependence structure. We propose a novel multivariate post-processing method based on generative machine learning where post-processed multivariate ensemble forecasts are generated from random noise, conditional on the inputs of raw ensemble forecasts. Moving beyond the two-step strategy of separately modeling marginal distributions and multivariate dependence structure, the generative modelling approach allows for directly obtaining multivariate probabilistic forecasts as output. The flexibility of the generative model also enables us to incorporate additional predictors straightforwardly and to generate an arbitrary number of post-processed ensemble members. In a case study on the surface temperature and wind speed forecasts from the European Centre of Medium-Range Weather Forecasts at weather stations in Germany, our generative model that incorporates additional weather predictors substantially improves upon the multivariate spatial forecasts from copula-based approaches. And the model shows competitive performance even with state-of-the-art neural network-based post-processing models applied for the marginal distributions.</p>

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