Econometrics and Finance Seminar: Gregor Kastner

Bayesian Estimation and Prediction of High-Dimensional Dynamic Covariance Matrices

Gregor KASTNER, University of Wien

Time-varying covariance estimation for multivariate time series suffers from the curse of dimensionality; as a consequence, parameter parsimony plays an important role in reliable statistical inference. The issue is addressed by modeling the underlying dynamics of a time series vector through a lower dimensional collection of latent factors that allow for time-varying stochastic volatilities. Furthermore, we apply a Normal-Gamma prior to the elements of the factor loadings matrix. This hierarchical shrinkage prior is a generalization of the Bayesian lasso and effectively pulls the factor loadings of unimportant factors towards zero, thereby increasing sparsity even more. To guarantee efficiency of the estimation procedure, we employ a fully Bayesian yet computationally feasible approach to obtain draws from the high-dimensional posterior and predictive distributions via Markov chain Monte Carlo (MCMC) samplers. We utilize several variants of an ancillarity-sufficiency interweaving strategy (ASIS) to boost efficiency when sampling the factor loadings as well as the parameters driving the time-varying volatilities. The effectiveness of the approach is demonstrated through extensive simulation studies. Furthermore, the model is applied to a 300-dimensional vector of stock returns to evaluate predictive performance for financial data. Additionally to being a stand-alone tool, the algorithm is designed to act as a "plug and play" extension for other MCMC samplers; it is implemented in the R package factorstochvol.