Bayesian shrinkage estimation of time-varying covariance matrices in financial time series

Mike K. P. SO, Wing Ki LIU, Man Ying Amanda CHU

Research output: Contribution to journalArticle


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. Copyright © 2018 Asia University, Taiwan.
Original languageEnglish
JournalAdvances in Decision Sciences
Issue numberA
Early online date16 Oct 2018
Publication statusPublished - Dec 2018


Shrinkage Estimation
Financial Time Series
Bayesian Estimation
Covariance matrix
Time series
Linear regression
Markov processes
Financial Modeling
Cholesky Decomposition
Stock Returns
Bayesian Analysis
Markov Chain Monte Carlo
Positive definite

Bibliographical note

So, M. K. P., Liu, W. K., & Chu, A. M. Y. (2018). Bayesian shrinkage estimation of time-varying covariance matrices in financial time series. Advances in Decision Sciences, 22(A). Retrieved from


  • Bayesian shrinkage
  • Dynamic correlations
  • Lasso
  • Markov chain Monte Carlo