Hysteretic Multivariate Bayesian Structural GARCH Model with Soft Information

2025-07-25

AI Summary

This paper addresses two key challenges in joint dynamic modeling of multiple financial time series: (1) insufficient integration of hard and soft information, and (2) difficulty in jointly capturing lagged effects and conditional heteroskedasticity. To this end, we propose a Lagged Multivariate Bayesian Structural GARCH model. Our method innovatively embeds soft information flexibly into the regime-switching component and develops a unified Bayesian estimation framework that integrates adaptive MCMC, spike-and-slab variable selection, and simulation-based smoothers—enhancing both parameter identifiability and model interpretability. Empirical results on the Dow Jones Industrial Average, NASDAQ Composite, and Semiconductor Index demonstrate that our model significantly outperforms mainstream benchmarks in goodness-of-fit and volatility forecasting accuracy. Notably, it improves characterization of market regime shifts and time-varying volatility dynamics.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

This study introduces the SH-MBS-GARCH model, a hysteretic multivariate Bayesian structural GARCH framework that integrates hard and soft information to capture the joint dynamics of multiple financial time series, incorporating hysteretic effects and addressing conditional heteroscedasticity through GARCH components. Various model specifications could utilize soft information to define the regime indicator in distinct ways. We propose a flexible, straightforward method for embedding soft information into the regime component, applicable across all SH-MBS-GARCH model variants. We further propose a generally applicable Bayesian estimation approach that combines adaptive MCMC, spike-and-slab regression, and a simulation smoother, ensuring accurate parameter estimation, validated through extensive simulations. Empirical analysis of the Dow Jones Industrial Average, NASDAQ Composite, and PHLX Semiconductor indices from January 2016 to December 2020 demonstrates that the SH-MBS-GARCH model outperforms competing models in fitting and prediction accuracy, effectively capturing regime-switching dynamics.

Problem

• Model captures joint dynamics of financial time series
• Integrates hard and soft information with GARCH
• Outperforms competitors in fitting and prediction

Innovation

• Hysteretic multivariate Bayesian GARCH model
• Integrates hard and soft information
• Bayesian estimation with adaptive MCMC