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A broad class of stochastic volatility models are defined by systems of stochastic differential equations, and while these models have seen widespread success in domains such as finance and statistical climatology, they typically lack an ability to condition on historical data to produce a true posterior distribution. To address this fundamental limitation, we show how to re-cast a class of stochastic volatility models as a hierarchical Gaussian process (GP) model with specialized covariance functions. This GP model retains the inductive biases of the stochastic volatility model while providing the posterior predictive distribution given by GP inference. Within this framework, we take inspiration from well studied domains to introduce a new class of models, Volt and Magpie, that significantly outperform baselines in stock and wind speed forecasting, and naturally extend to the multitask setting.
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This content will become publicly available on May 1, 2026
Dependence properties of stochastic volatility models
The concepts of physical dependence and approximability have been extensively used over the past two decades to quantify nonlinear dependence in time series. We show that most stochastic volatility models satisfy both dependence conditions, even if their realizations take values in abstract Hilbert spaces, thus covering univariate, multi‐variate and functional models. Our results can be used to apply to general stochastic volatility models a multitude of inferential procedures established for Bernoulli shifts.
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- PAR ID:
- 10582746
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Journal of Time Series Analysis
- Volume:
- 46
- Issue:
- 3
- ISSN:
- 0143-9782
- Page Range / eLocation ID:
- 421 to 431
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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