Embracing Heteroscedasticity for Probabilistic Time Series Forecasting

2026-03-25

AI Summary

This work addresses the limitation of existing non-autoregressive time series forecasting methods, which typically rely on mean squared error and implicitly assume homoscedasticity, thereby failing to capture the time-varying heteroscedasticity inherent in real-world data. To overcome this, we propose the Location-Scale Gaussian Variational Autoencoder (LSG-VAE), which explicitly models time-dependent means and variances within a non-autoregressive generative framework for the first time. Our approach incorporates an adaptive decay mechanism that automatically downweights the influence of high-volatility observations during training, effectively mitigating their disruptive impact. Extensive experiments demonstrate that LSG-VAE consistently outperforms 15 strong baselines across nine benchmark datasets, achieving superior prediction accuracy, reliable uncertainty quantification, and efficient inference—thus breaking free from the restrictive homoscedastic assumption.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• heteroscedasticity
• probabilistic time series forecasting
• time-varying variance
• nonstationary dynamics
• uncertainty quantification

Innovation

• heteroscedasticity
• probabilistic time series forecasting
• location-scale likelihood
• variational autoencoder
• aleatoric uncertainty