Sparse Bayesian time-varying covariance estimation in many dimensions

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Abstract
Dynamic covariance estimation for multivariate time series suffers from the curse of dimensionality. This renders parsimonious estimation methods essential for conducting reliable statistical inference. In this paper, the issue is addressed by modeling the underlying co-volatility dynamics of a time series vector through a lower dimensional collection of latent time-varying stochastic factors. Furthermore, we apply a Normal-Gamma prior to the elements of the factor loadings matrix. This hierarchical shrinkage prior effectively pulls the factor loadings of unimportant factors towards zero, thereby increasing parsimony even more. We apply the model to simulated data as well as daily log-returns of 300 S&P 500 stocks and demonstrate the effectiveness of the shrinkage prior to obtain sparse loadings matrices and more precise correlation estimates. Moreover, we investigate predictive performance and discuss different choices for the number of latent factors. Additionally to being a stand-alone tool, the algorithm is designed to act as a "plug and play" extension for other MCMC samplers.

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