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 .
We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for the elements of the factor loadings matrix pulls loadings on superfluous factors towards zero . To demonstrate the merits of the proposed framework, the model is applied to simulated data as well as to daily log-returns of 300 S&P 500 members. Our approach yields precise correlation estimates , strong implied minimum variance portfolio performance and superior forecasting accuracy in terms of log predictive scores when compared to typical benchmarks .
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and superior forecasting accuracy in terms of log predictive scores when compared to typical benchmarks