Embracing Heteroscedasticity for Probabilistic Time Series Forecasting
Summary: arXiv:2603.24254v1 Announce Type: cross
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.
The Challenge of Heteroscedasticity
However, most existing non-autoregressive generative approaches to PTSF, such as TimeVAE and K2VAE, rely on MSE-based training objectives that implicitly impose a homoscedastic assumption. This fundamental limitation restricts their ability to model temporal heteroscedasticity effectively.
Introducing the Location-Scale Gaussian VAE (LSG-VAE)
To address the aforementioned limitations, researchers propose the Location-Scale Gaussian VAE (LSG-VAE). This framework is both simple and effective, as it explicitly parameterizes both the predictive mean and time-dependent variance through a location-scale likelihood formulation.
Key Features of LSG-VAE
- Heteroscedastic Aleatoric Uncertainty: LSG-VAE is designed to capture the complexities of heteroscedasticity by modeling the varying uncertainty associated with different time points.
- Adaptive Attenuation Mechanism: This feature allows the model to automatically down-weight highly volatile observations during training, thus improving robustness in trend prediction.
- Real-Time Deployment: The framework maintains high computational efficiency, making it suitable for real-time applications.
Experimental Validation
Extensive experiments conducted on nine benchmark datasets have demonstrated that LSG-VAE consistently outperforms fifteen strong generative baselines. The results indicate a significant improvement in forecasting accuracy while effectively managing uncertainty.
Conclusion
The introduction of the Location-Scale Gaussian VAE represents a significant advancement in the field of probabilistic time series forecasting. By embracing heteroscedasticity and addressing the limitations of existing methods, LSG-VAE paves the way for more accurate and reliable predictive models. As the demand for precise forecasting in various domains continues to grow, the adoption of such innovative approaches will be crucial for enhancing decision-making processes across industries.