The paper introduces Wasserstein Exponential Smoothing (WES), a single‑parameter recursive method for forecasting distributional time series on ℝ. WES updates forecast distributions along Wasserstein geodesics, allowing direct application to empirical distributions without parametric modeling. In high‑frequency equity‑index return and household electricity‑demand data, WES achieves the lowest one‑step‑ahead Wasserstein prediction error among existing benchmarks and is retained in the 90% model confidence set for all 20 series examined.
arXiv:2607. 02623v1 Announce Type: new Abstract: Time series foundation models (TSFMs) have shown strong zero-shot forecasting performance, but their generalization in covariate-driven, non-stationary settings is underexplored.
arXiv:2606. 30310v1 Announce Type: cross Abstract: The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections.
arXiv:2608. 11114v1 Announce Type: cross Abstract: Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings.
arXiv:2605. 29072v2 Announce Type: replace Abstract: Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management.
arXiv:2604. 18546v2 Announce Type: replace Abstract: We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y.
The paper presents an online algorithm for multivariate distributional regression tailored to high‑dimensional probabilistic electricity price forecasting. It models conditional means, variances, and dependence structures of 24‑hour day‑ahead prices using coordinate descent and LASSO regularization, enabling scalable estimation in large covariate spaces. A regularized estimation path allows early stopping to prevent overfitting, and the method delivers interpretable, well‑calibrated joint prediction intervals, outperforming benchmarks on German market data.
The paper introduces two methods for modelling aggregated supply and demand curves in the EPEX SPOT Day‑Ahead market. The first is a low‑dimensional parametric approach that produces deterministic point forecasts using plateau levels, elastic‑region boundaries, polynomial coefficients, and XGBoost. The second is a high‑dimensional generative approach based on conditional Denoising Diffusion Probabilistic Models that samples plausible curves from price arrivals and volume‑increment marks, enabling analysis of price and volume sensitivity and price impact.
arXiv:2603.07014v2 Announce Type: replace-cross Abstract: Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univ...
arXiv:2605. 29072v3 Announce Type: replace Abstract: Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management.
Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction.
Halo is a modification to existing deep forecasters that adds a second output for estimating the scale of the predicted distribution, trained with a matching negative log likelihood. Experiments on five electricity price markets show that Halo improves mean squared error and mean absolute error in 28 of 30 model‑market‑metric comparisons, with average MSE reductions of 2.6% to 16.5% and MAE reductions of 1.7% to 11.0%. The study finds that the source of the scale estimate is less important than the fact that the network estimates scale, and that the improvement persists without retuning hyperparameters.
arXiv:2608. 13418v1 Announce Type: cross Abstract: Given a dataset where a portion of the samples are contaminated, our goal is to recover the underlying clean population distribution.