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Abstract:
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Gaussian graphical models are widely popular for studying the conditional dependence among random variables. However, time series data present additional challenges: the graphs can evolve over time, and the data often exhibit heavy-tailed characteristics. To address these challenges, we propose dynamic and robust Bayesian graphical models. Building upon state-of-the-art Bayesian graphical models for non-dynamic data, we introduce dynamics via a hidden Markov model (HMM), which provides a principled way to cluster time points and identify change points in the graph. The HMM latent states are linked both temporally and hierarchically for greater information sharing across time and between states. For model robustness, we replace the Gaussian assumption with heavy-tailed alternatives based on the multivariate t-distribution. The proposed methods are computationally efficient and demonstrate excellent graph estimation for simulated data with substantial improvements over non-robust graphical models. We apply the proposed approach to study the U.S. futures market and discover meaningful hidden states, including a new characterization of the futures market the initial peak of COVID-19.
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