Embracing Heteroscedasticity for Probabilistic Time Series Forecasting

• URL: http://arxiv.org/abs/2603.24254v1
• Date: Wed, 25 Mar 2026 12:48:50 GMT
• Title: Embracing Heteroscedasticity for Probabilistic Time Series Forecasting
• Abstract summary: Location-Scale Gaussian VAE (LSG-VAE) is a simple but effective framework that explicitly parameterizes both the predictive mean and time-dependent variance.<n>LSG-VAE consistently outperforms fifteen strong generative baselines while maintaining high computational efficiency suitable for real-time deployment.
• Score: 22.43559255963294
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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