Dynamic covariance estimation for multivariate time series suffers from the curse of dimensionality; this renders parsimonious approaches essential for conducting reliable statistical inference. We address this issue by modeling the underlying 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 is a generalization of the Bayesian lasso and effectively pulls the factor loadings of unimportant factors towards zero, thereby increasing sparsity even more. Estimation is carried out via Bayesian MCMC methods that allow to obtain draws from the high-dimensional posterior and predictive distributions. To guarantee efficiency of the samplers, we utilize several variants of an ancillarity-sufficiency interweaving strategy (ASIS) for sampling the factor loadings. Through extensive simulation studies, we demonstrate the effectiveness of the approach. Furthermore, we apply the model to a 20-dimensional exchange rate series and a 300-dimensional vector of stock returns to evaluate predictive performance.
21 Mai 2015 → 22 Mai 2015
2nd Vienna Workshop on High-Dimensional Time Series in Macroeconomics and Finance
Österreichische Systematik der Wissenschaftszweige (ÖFOS)