# BAYESIAN ANALYSIS OF MULTIVARIATE REGIME SWITCHING COVARIANCE MODEL

Open Access
Author:
Zhang, Lu
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
October 23, 2009
Committee Members:
• John Liechty, Committee Chair
• Runze Li, Committee Member
• Murali Haran, Committee Member
• Timothy Simin, Committee Member
• James Landis Rosenberger, Committee Member
Keywords:
• dynamic covariance
• state space model
• Markov Chain Monte Carlo (MCMC)
• bayesian analysis
• stochastic volatility
• time series analysis
Abstract:
We propose a new multivariate regime switching covariance model, where the covariances are decomposed into volatilities and correlations, both of which are regime switching. The model specifies an independent regime switching process for the volatilities of each asset, and one process for the correlation matrix. It is the first time that the volatility and correlation regimes are modeled simultaneously. From an in-sample perspective, it helps identify the relationship between the volatility and correlation dynamics. From a forward looking perspective, this model can potentially make good forecast of financial crisis where the market enters a high volatility and high correlation regime at the same time. Our model, along with the proposed Markov Chain Monte Carlo (MCMC) methods, contributes to solving three important technical issues. First, we model the unobserved regime switching process by a jump chain and waiting times between jumps. We can use both Exponential and Gamma distribution to describe the waiting time. This specification allows us to generalize the hidden regime process to be non-Markovian, which provides a better fit for empirical data that have seasonal switches in volatility levels. Secondly, we use a shrinkage model for the off-diagonal elements of the correlation matrix, which imposes an average correlation on each regime. This allows us to clearly represent and identify the latent correlation regimes. Third, since missing data is a challenge in real data analysis, we introduce a Bayesian imputation method which can accurately recover missing values, which can occur for example over different holidays for indices from different countries. Based on the structure of our model, we also introduce a portfolio allocation strategy where a portfolio manager re-balances portfolio weights whenever a switch in regime is detected. Such a strategy keeps a good balance between stock return and risk, and at the same time saves portfolio adjustment cost. We discuss examples on simulated data set, natural gas commodity data and weekday international market indices.