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

Title

BAYESIAN SHRINKAGE ESTIMATION OF TIME-VARYING COVARIANCE MATRICES IN FINANCIAL TIME SERIES

Authors

Mike K. P. So
(Department of Information Systems, Business Statistics and Operations Management, Hong Kong University of Science and Technology)
Wing Ki Liu
(Department of Information Systems, Business Statistics and Operations Management, Hong Kong University of Science and Technology)
Amanda M. Y. Chu
(Department of Social Sciences, Education University of Hong Kong)

Abstract

Modeling financial returns is challenging because the correlations and variance of returnsare 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.

Keywords

Bayesian shrinkage; dynamic correlations; GARCH; lasso; Markov chain Monte Carlo

Classification-JEL

C11, C32, C58, G17, G32

Pages

369-404

https://doi.org/10.47654/v22y2018i1p369-404