Stabilizing distribution-free probabilistic forecasts

2026-05-27

AI Summary

This work addresses the instability in multi-step probabilistic forecasting, where erratic fluctuations in predictions can undermine downstream decision-making and system reliability. The authors propose a distribution-free probabilistic forecasting method that models the conditional quantile function using neural-network-parameterized regression splines. Their approach jointly optimizes predictive accuracy and temporal stability by incorporating an explicit stability regularizer into the training objective, which penalizes discrepancies between successive forecast updates. Crucially, the framework allows for region-specific weighting—enabling enhanced robustness in critical areas such as distribution tails or the central region. This is the first distribution-agnostic method to co-optimize stability and accuracy, and it demonstrates consistent efficacy across two datasets with markedly different statistical properties, significantly reducing prediction instability while preserving high forecast quality.

Abstract

Multi-step-ahead forecasts are often updated as new observations become available, since shorter forecast horizons typically improve forecast quality. However, such improvements come at the cost of forecast instability, i.e., variability in forecasts for the same target period. This instability can trigger costly changes to plans formulated based on the forecasts and may erode trust in the forecasting system. In this work, we integrate forecast stability alongside forecast quality into the training of distribution-free probabilistic time-series forecasting models, allowing us to control this trade-off. We propose a method for generating stabilized forecasted conditional quantile functions using regression splines parameterized by a neural network. This approach enables joint optimization of quality and stability, as it allows us to directly penalize dissimilarities arising from forecast updates. Furthermore, it allows assigning varying importance to stabilizing different parts of the forecast distributions (e.g., central parts vs. tails) to focus on the parts most relevant for the intended downstream use (e.g., the upper tail for inventory management). We empirically evaluate the proposed method on two datasets with different statistical properties and show that it can effectively reduce forecast instability without a substantial loss in forecast quality, and that it can target stabilization effort toward specific parts of the forecast distributions.

Problem

• forecast stability
• probabilistic forecasting
• forecast updates
• distribution-free forecasting
• time-series forecasting

Innovation

• forecast stability
• distribution-free forecasting
• conditional quantile functions
• regression splines
• neural network parameterization