Beyond Static Uncertainty: Modeling Temporal Uncertainty Dynamics for Probabilistic Time Series Forecasting
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| Format: | Preprint |
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2026
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| _version_ | 1866917548011814912 |
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| author | Wang, Yijun Zhuang, Qiyuan Marchanka, Larysa Wei, Xiu-Shen |
| author_facet | Wang, Yijun Zhuang, Qiyuan Marchanka, Larysa Wei, Xiu-Shen |
| contents | Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate predictive uncertainty as an independent per-step quantity, leaving the evolution and persistence of volatility regimes under-modeled. We formalize this missing dimension as temporal uncertainty dynamics and instantiate it in the Volatility Dynamics Variational Autoencoder (VolDy-VAE), a non-autoregressive generative forecaster with a location-scale decoder. VolDy-VAE combines a location path for mean prediction with a recurrent scale path that transfers and evolves a volatility hidden state from the look-back window to the forecasting horizon, enabling temporally coherent predictive variances. This design yields an adaptive attenuation mechanism: high-variance observations receive lower influence on the location estimate while their uncertainty is preserved through explicit scale predictions. We further provide a simplified regime-switching analysis showing that, when variances are known or consistently estimated, the volatility-aware objective reduces to inverse-variance weighting, whereas MSE-based estimators remain unbiased but statistically inefficient. Experiments on nine benchmarks show that VolDy-VAE improves forecasting accuracy and uncertainty calibration over competitive probabilistic and point-forecasting baselines while maintaining low inference latency; plug-in studies further indicate that the VolDy principle can benefit GAN, Koopman VAE, and Transformer backbones. The source code is publicly available at https://github.com/wangyijunlyy/VolDy-VAE. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond Static Uncertainty: Modeling Temporal Uncertainty Dynamics for Probabilistic Time Series Forecasting Wang, Yijun Zhuang, Qiyuan Marchanka, Larysa Wei, Xiu-Shen Machine Learning Artificial Intelligence Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate predictive uncertainty as an independent per-step quantity, leaving the evolution and persistence of volatility regimes under-modeled. We formalize this missing dimension as temporal uncertainty dynamics and instantiate it in the Volatility Dynamics Variational Autoencoder (VolDy-VAE), a non-autoregressive generative forecaster with a location-scale decoder. VolDy-VAE combines a location path for mean prediction with a recurrent scale path that transfers and evolves a volatility hidden state from the look-back window to the forecasting horizon, enabling temporally coherent predictive variances. This design yields an adaptive attenuation mechanism: high-variance observations receive lower influence on the location estimate while their uncertainty is preserved through explicit scale predictions. We further provide a simplified regime-switching analysis showing that, when variances are known or consistently estimated, the volatility-aware objective reduces to inverse-variance weighting, whereas MSE-based estimators remain unbiased but statistically inefficient. Experiments on nine benchmarks show that VolDy-VAE improves forecasting accuracy and uncertainty calibration over competitive probabilistic and point-forecasting baselines while maintaining low inference latency; plug-in studies further indicate that the VolDy principle can benefit GAN, Koopman VAE, and Transformer backbones. The source code is publicly available at https://github.com/wangyijunlyy/VolDy-VAE. |
| title | Beyond Static Uncertainty: Modeling Temporal Uncertainty Dynamics for Probabilistic Time Series Forecasting |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2603.24254 |