We introduce a novel Bayesian framework for estimating time-varying volatility by extending the Random Walk Stochastic Volatility (RWSV) model with Dynamic Shrinkage Processes (DSP) in log-variances. Unlike the classical Stochastic Volatility (SV) 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. We further enhance the model by incorporating a nugget effect, allowing it to flexibly capture small-scale variability while preserving smoothness elsewhere. We derive the theoretical properties of the global-local shrinkage prior DSP. Through simulation studies, we show that ASV exhibits remarkable misspecification resilience and low prediction error across various data-generating processes. Furthermore, ASV's capacity to yield locally smooth and interpretable estimates facilitates a clearer understanding of the underlying patterns and trends in volatility. As an extension, we develop the Bayesian Trend Filter with ASV (BTF-ASV) which allows joint modeling of the mean and volatility with abrupt changes. Finally, our proposed models are applied to time series data from finance, econometrics, and environmental science, highlighting their flexibility and broad applicability.

翻译：本文提出了一种新颖的贝叶斯框架，通过在随机游走随机波动率（RWSV）模型的对数方差中引入动态收缩过程（DSP），以估计时变波动率。与经典的随机波动率（SV）模型或具有严格参数平稳性假设的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波动率演化及其不确定性的估计。我们进一步通过引入块金效应来增强模型，使其能够灵活捕捉小尺度变异，同时在其余区域保持平滑性。我们推导了全局-局部收缩先验DSP的理论性质。通过模拟研究，我们证明ASV在各种数据生成过程中表现出卓越的模型误设稳健性和较低的预测误差。此外，ASV能够生成局部平滑且可解释的估计，有助于更清晰地理解波动率的内在模式与趋势。作为扩展，我们开发了基于ASV的贝叶斯趋势滤波（BTF-ASV），该模型允许对存在突变的均值与波动率进行联合建模。最后，我们将所提出的模型应用于金融、计量经济学和环境科学的时间序列数据，突显了其灵活性与广泛的适用性。