Smoothing Variances Across Time: Adaptive Stochastic Volatility

2024-08-21

AI Summary

This paper addresses the challenge of simultaneously achieving smoothness and dynamic adaptability in time-varying volatility estimation. We propose the Adaptive Stochastic Volatility (ASV) model, which introduces a Dynamic Shrinkage Process (DSP) on the log-variance to relax the strong stationarity assumptions inherent in classical stochastic volatility (SV) and GARCH models. ASV is the first framework to integrate global–local shrinkage priors into dynamic variance modeling, yielding theoretical interpretability, robustness to model misspecification, and joint Bayesian mean–variance trend filtering. Leveraging Bayesian inference and stochastic volatility principles, ASV accurately captures fine-scale volatility fluctuations while preserving coarse-scale smoothness. Simulation studies and empirical analyses across finance, environmental science, and epidemiology demonstrate substantial reductions in predictive error and robust estimation of volatility-of-volatility (vol-of-vol).

Technology Category

• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

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.

Problem

• Estimating time-varying volatility adaptively
• Capturing small-scale variability with smoothness
• Modeling mean and volatility with abrupt changes

Innovation

• Bayesian framework with Dynamic Shrinkage Processes
• Adaptive Stochastic Volatility for smooth estimates
• Nugget effect captures small-scale variability