Learning the Probability Distributions of Day-Ahead Electricity Prices

We propose a novel machine learning approach for probabilistic forecasting of hourly day-ahead electricity prices. In contrast with the recent advances in data-rich probabilistic forecasting, which approximates distributions with few features (such as moments), our method is nonparametric and selects the distribution from all possible empirical distributions learned from the input data without the need for limiting assumptions. The model that we propose is a multioutput neural network that accounts for the temporal dynamics of the probabilities and controls for monotonicity using a penalty. Such a distributional neural network can precisely learn complex patterns from many relevant variables that affect electricity prices. We illustrate the capacity of the developed method on German hourly day-ahead electricity prices and predict their probability distribution via many variables, doing so more accurately than the state-of-the-art benchmarks can, thus revealing new valuable information in the data.