Bayesian Shrinkage Estimation of Time-varying Covariance Matrices in Financial Time Series

Modeling financial returns is challenging because the correlations and variance of returns are time-varying and the covariance matrices can be quite high-dimensional. In this paper, we develop a Bayesian shrinkage approach with modified Cholesky decomposition to model correlations between financial returns. We reparameterize the correlation parameters to meet their positive definite constraint for Bayesian analysis. To implement an efficient sampling scheme in posterior inference, hierarchical representation of Bayesian lasso is used to shrink unknown coefficients in linear regressions. Simulation results show good sampling properties that iterates from Markov chain Monte Carlo converge quickly. Using a real data example, we illustrate the application of the proposed Bayesian shrinkage method in modeling stock returns in Hong Kong.