Embracing Heteroscedasticity for Probabilistic Time Series Forecasting

TL;DR

This paper introduces LSG-VAE, a novel probabilistic time series forecasting model that explicitly models heteroscedasticity, improving uncertainty quantification and robustness over existing methods.

Contribution

The paper proposes LSG-VAE, a location-scale Gaussian VAE that captures time-varying variance in time series, addressing limitations of MSE-based training in existing models.

Findings

LSG-VAE outperforms 15 baselines on 9 datasets.

It effectively models heteroscedastic uncertainty.

The approach is computationally efficient for real-time use.

Abstract

Probabilistic time series forecasting (PTSF) aims to model the full predictive distribution of future observations, enabling both accurate forecasting and principled uncertainty quantification. A central requirement of PTSF is to embrace heteroscedasticity, as real-world time series exhibit time-varying conditional variances induced by nonstationary dynamics, regime changes, and evolving external conditions. However, most existing non-autoregressive generative approaches to PTSF, such as TimeVAE and $K^2$VAE, rely on MSE-based training objectives that implicitly impose a homoscedastic assumption, thereby fundamentally limiting their ability to model temporal heteroscedasticity. To address this limitation, we propose the Location-Scale Gaussian VAE (LSG-VAE), a simple but effective framework that explicitly parameterizes both the predictive mean and time-dependent variance through a location-scale likelihood formulation. This design enables LSG-VAE to faithfully capture heteroscedastic aleatoric uncertainty and introduces an adaptive attenuation mechanism that automatically down-weights highly volatile observations during training, leading to improved robustness in trend prediction. Extensive experiments on nine benchmark datasets demonstrate that LSG-VAE consistently outperforms fifteen strong generative baselines while maintaining high computational efficiency suitable for real-time deployment.