We introduce a novel Bayesian framework for estimating time-varying volatility by extending the Random Walk Stochastic Volatility (RWSV) model with a new Dynamic Shrinkage Process (DSP) in (log) variances. Unlike classical Stochastic Volatility or GARCH-type models with restrictive parametric stationarity assumptions, our proposed Adaptive Stochastic Volatility (ASV) model provides smooth yet dynamically adaptive estimates of evolving volatility and its uncertainty (vol of vol). We derive the theoretical properties of the proposed global-local shrinkage prior. Through simulation studies, we demonstrate that ASV exhibits remarkable misspecification resilience with low prediction error across various data generating scenarios in simulation. Furthermore, ASV's capacity to yield locally smooth and interpretable estimates facilitates a clearer understanding of underlying patterns and trends in volatility. Additionally, we propose and illustrate an extension for Bayesian Trend Filtering simultaneously in both mean and variance. Finally, we show that this attribute makes ASV a robust tool applicable across a wide range of disciplines, including in finance, environmental science, epidemiology, and medicine, among others.

翻译：我们提出了一种新颖的贝叶斯框架，通过将随机游走随机波动率（RWSV）模型扩展为具有新的（对数）方差动态收缩过程（DSP），来估计时变波动率。与具有限制性参数平稳性假设的经典随机波动率或GARCH类模型不同，我们提出的自适应随机波动率（ASV）模型能够提供平滑且动态自适应的演化波动率及其不确定性（波动率的波动率）估计。我们推导了所提出的全局-局部收缩先验的理论性质。通过模拟研究，我们证明ASV在模拟的各种数据生成场景中表现出显著的模型误设稳健性和较低的预测误差。此外，ASV能够产生局部平滑且可解释的估计，这有助于更清晰地理解波动率的基本模式和趋势。此外，我们提出并阐述了一种在均值和方差中同时进行贝叶斯趋势滤波的扩展方法。最后，我们展示了这一特性使得ASV成为一个适用于广泛学科的稳健工具，包括金融、环境科学、流行病学和医学等领域。