Fast Computation of Randomly Walking Volatility with Chained Gamma Distributions

Volatility clustering is a ubiquitous phenomenon in financial time series analysis. In this study, we propose a Dynamic Bayesian Network (DBN) that leverages the conjugate prior relationships of normal-gamma and gamma-gamma distributions, preserving local posterior invariance at each node within the network. By incorporating dummy gamma nodes, we ensure that the model’s volatility follows an independent incremental process. This proposed model offers two distinct advantages: (1) it exhibits heavier tails (manifesting as positive excess kurtosis) compared to Gaussian distributions, thereby contrasting sharply with conventional linear models; (2) it utilizes Variational Inference (VI) to expedite state estimation relative to Monte Carlo (MC) methods, ensuring deterministic convergence. In comparative experiments involving eight established methodologies and four variations of our approach across eight datasets, we observed the following: (1) When employing MC, our model achieves volatility forecasting performance comparable to leading methods; (2) when utilizing only VI, it attains acceptable accuracy, particularly for high-frequency data, albeit slightly lower than the state-of-the-art; (3) notably, VI reduces the runtime of our Gam-Chain model to generally less than 5% of that of MC-based methods.