NBMLSS: probabilistic forecasting of electricity prices via Neural Basis Models for Location Scale and Shape

TL;DR

NBMLSS tackles probabilistic, multi-horizon electricity price forecasting by extending Neural Additive Models to Location, Scale and Shape (NAMLSS) with a shared basis of feature shape functions that are combined via linear projections into $H$-step distribution parameters for each horizon $h$ and parameter $p$. The approach uses a Johnson’s SU density, end-to-end training with negative log-likelihood, and optional RevIN-based drift handling, benchmarking against distributional neural networks on European day-ahead markets. Results show NBMLSS achieves competitive CRPS and calibration, with the JSU parameterization providing superior flexibility in volatile regimes and offering interpretable shape-function maps that reveal feature-to-parameter relationships. The work demonstrates interpretable, scalable probabilistic forecasts that can support decision-making in electricity markets, and outlines future directions such as conformal inference and feature-deconvolution to further enhance reliability and insight.

Abstract

Forecasters using flexible neural networks (NN) in multi-horizon distributional regression setups often struggle to gain detailed insights into the underlying mechanisms that lead to the predicted feature-conditioned distribution parameters. In this work, we deploy a Neural Basis Model for Location, Scale and Shape, that blends the principled interpretability of GAMLSS with a computationally scalable shared basis decomposition, combined by linear projections supporting dedicated stepwise and parameter-wise feature shape functions aggregations. Experiments have been conducted on multiple market regions, achieving probabilistic forecasting performance comparable to that of distributional neural networks, while providing more insights into the model behavior through the learned nonlinear feature level maps to the distribution parameters across the prediction steps.

Figures (19)

• Figure 1: NBMLSS schema
• Figure 2: Shape functions of 3 ensemble components on past price features (DE-h8-loc)
• Figure 3: Shape functions of 3 ensemble components on exogenous features (DE-h16-loc)
• Figure 4: Samples of predicted distribution deciles on DE market of 3 ensemble components
• Figure 5: Shape functions of the JSU location parameter on the masked exogenous subsets (3 ensemble components on DE)