[Paper Review] A Dynamic Bayesian Model for Interpretable Decompositions of Market Behaviour

Théophile Griveau-Billion, Ben Calderhead|arXiv (Cornell University)|Apr 17, 2019

Market Dynamics and VolatilityEconomics, Econometrics and Finance21 references3 citations

TL;DR

This paper proposes a Dynamic Bayesian model, the Heterogeneous Simultaneous Graphical Dynamic Linear Model (H-SGDLM), which decomposes multivariate market volatility into interpretable endogenous and exogenous factors using a GPU-scalable framework. By integrating the HAR-RV model into a dynamic graphical structure, it improves long-term volatility forecasting—achieving 65.93% accuracy in predicting large moves in S&P 500 stocks over 18 years, outperforming standard HAR-RV and SGDLM models.

ABSTRACT

We propose a heterogeneous simultaneous graphical dynamic linear model (H-SGDLM), which extends the standard SGDLM framework to incorporate a heterogeneous autoregressive realised volatility (HAR-RV) model. This novel approach creates a GPU-scalable multivariate volatility estimator, which decomposes multiple time series into economically-meaningful variables to explain the endogenous and exogenous factors driving the underlying variability. This unique decomposition goes beyond the classic one step ahead prediction; indeed, we investigate inferences up to one month into the future using stocks, FX futures and ETF futures, demonstrating its superior performance according to accuracy of large moves, longer-term prediction and consistency over time.

Motivation & Objective

• To develop a scalable, interpretable model that decomposes market volatility into endogenous (asset-specific) and exogenous (market-wide) drivers.
• To extend the standard SGDLM framework by incorporating the heterogeneous autoregressive realised volatility (HAR-RV) model for improved multivariate volatility estimation.
• To enable long-horizon forecasting—up to one month ahead—by leveraging time-evolving coefficient dynamics from Kalman filtering.
• To create economically meaningful signals through coefficient decomposition that enhance market stress and large move prediction.
• To ensure robustness and consistency of predictions across different market regimes through time-varying, sparse multivariate modeling.

Proposed method

• The H-SGDLM model combines the HAR-RV model with a Simultaneous Graphical Dynamic Linear Model (SGDLM), allowing each asset's log-volatility to be modeled as a DLM with idiosyncratic, cross-series, and specific factors.
• The model uses a Normal-Gamma conjugate prior for the state vector and precision, enabling efficient sequential Bayesian updating via Kalman filter equations.
• A variational Bayes approximation is applied to decouple the multivariate posterior into conditionally independent Normal-Gamma components, enabling GPU scalability.
• State evolution is modeled via a random walk with block discounting: external (exogenous) and parent (endogenous) variables are updated with distinct discount factors δφ and δγ.
• The model employs a scale space change point algorithm to detect structural shifts in coefficient dynamics, enhancing predictive reliability for large moves.
• Predictions are generated by sampling from the predictive distribution using transformed state means and covariance matrices derived from the inverse of the system matrix (I−Γ)−1.

Experimental results

Research questions

• RQ1 Can a dynamic Bayesian model decompose multivariate market volatility into economically interpretable endogenous and exogenous components?
• RQ2 Does integrating the HAR-RV model into a dynamic graphical structure improve long-term volatility forecasting accuracy, especially for large moves?
• RQ3 Can the model consistently predict market stress indicators weeks in advance, beyond one-step-ahead forecasts?
• RQ4 How do time-varying coefficients and their decomposition into endogenous/exogenous factors improve predictive performance over time?
• RQ5 To what extent does the model’s performance remain stable across different market regimes and asset classes?

Key findings

• The H-SGDLM model correctly predicted 63.89% of large positive variance moves (>9.28%) in 487 European stocks over 18 years (2001–2019), significantly outperforming HAR-RV (53.24%) and standard SGDLM (34.69%).
• In the S&P 500 universe over the same period, the model achieved 65.93% accuracy in predicting large variance moves, demonstrating strong generalization across markets.
• The model’s predictive performance for large moves remained consistent over time, as confirmed by backtesting, indicating robustness to changing market conditions.
• The decomposition of coefficients into endogenous and exogenous factors generated new, reliable signals that enhanced long-term inference and stress forecasting.
• The model’s predictive distribution captured more than 68% of large negative moves, and the confidence interval coverage was tighter for large moves when using the new decomposition.
• The GPU-parallelized inference pipeline enabled efficient scaling across thousands of assets, making the model suitable for real-time market monitoring and risk management applications.