# Stabilizing distribution-free probabilistic forecasts

arXiv: https://arxiv.org/abs/2605.28531 · HTML: https://mlsanity.com/paper/2605.28531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Exponential Moving Average of Weights in Deep Learning: Dynamics and Benefits](https://mlsanity.com/paper/2411.18704/) (2024)
- [Meta-learning framework with applications to zero-shot time-series forecasting](https://mlsanity.com/paper/2002.02887/) (2020)
- [Criteria for Classifying Forecasting Methods](https://mlsanity.com/paper/2212.03523/) (2022)
- [Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting](https://mlsanity.com/paper/2111.06581/) (2021)
- [Probabilistic Time Series Forecasting with Implicit Quantile Networks](https://mlsanity.com/paper/2107.03743/) (2021)
- [ARMDN: Associative and Recurrent Mixture Density Networks for eRetail Demand Forecasting](https://mlsanity.com/paper/1803.03800/) (2018)
- [Continuous and Distribution-free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach](https://mlsanity.com/paper/2206.02433/) (2022)
- [On Forecast Stability](https://mlsanity.com/paper/2310.17332/) (2023)
- [Using dynamic loss weighting to boost improvements in forecast stability](https://mlsanity.com/paper/2409.18267/) (2024)

## Abstract (arXiv)

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.