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. Consequently, parsimonious estimation methods are essential for conducting reliable statistical inference. In the paper at hand, this 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 propose using a Normal-Gamma prior for 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 its effectiveness to obtain sparse loadings matrices and more precise correlation estimates. To assess predictive accuracy, our approach is compared to more traditional approaches via log predictive scores and implied minimum variance portfolio performance. Thereby, different choices for the number of latent factors are discussed. In addition to serving as a stand-alone tool, the algorithm is designed to complement other MCMC samplers as a "plug and play" extension. It can easily be used by means of the R package factorstochvol.

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