Stochastic Volatility in Mean Models with Heavy Tails: A Fast Approximate Bayesian Inference Using Hidden Markov Models

2026-06-21

AI Summary

This study addresses the computational challenges and inefficiency associated with Bayesian inference for stochastic volatility mean models under heavy-tailed distributions. To overcome these limitations, the authors extend the model to the class of scale mixtures of normal distributions and develop a fast approximate Bayesian inference framework based on hidden Markov models. By leveraging special functions to circumvent numerical integration and incorporating parallel computing strategies, the proposed approach substantially enhances both algorithmic stability and computational efficiency. The method achieves inference accuracy comparable to that of conventional Markov chain Monte Carlo (MCMC) techniques while accelerating computation by approximately an order of magnitude, thereby offering an efficient and practical Bayesian solution for modeling high-dimensional financial time series.

Abstract

This paper extends the approximate Bayesian estimation framework for Stochastic Volatility in Mean (SVM) models to accommodate heavy-tailed distributions from the Scale Mixture of Normals (SMN) family. To overcome the computational challenges arising from these models, we propose a numerically stable estimation procedure that exploits special functions to eliminate the need for direct numerical integration. Furthermore, the implementation incorporates parallel computing strategies that substantially reduce computational costs. Simulation studies and empirical applications demonstrate that the proposed approach delivers accurate inference while achieving computational times that are approximately an order of magnitude smaller than those required by conventional Markov chain Monte Carlo (MCMC) methods.

Problem

• Stochastic Volatility in Mean
• Heavy Tails
• Approximate Bayesian Inference
• Scale Mixture of Normals
• Computational Efficiency

Innovation

• Stochastic Volatility in Mean
• Heavy-tailed distributions
• Approximate Bayesian inference
• Hidden Markov Models
• Parallel computing