Modeling Multivariate Volatility Processes: Theory and Evidence

Abstract

This article presents theoretical and empirical methodology for estimation and modeling of multivariate volatility processes. It surveys the model specifications and the estimation methods. Multivariate GARCH models covered are VEC (initially due to Bollerslev, Engle and Wooldridge, 1988), diagonal VEC (DVEC), BEKK (named after Baba, Engle, Kraft and Kroner, 1995), Constant Conditional Correlation Model (CCC, Bollerslev, 1990), Dynamic Conditional Correlation Model (DCC models of Tse and Tsui, 2002, and Engle, 2002). I illustrate approach by applying it to daily data from the Belgrade stock exchange, I examine two pairs of daily log returns for stocks and index, report the results obtained, and compare them with the restricted version of BEKK, DVEC and CCC representations. The methods for estimation parameters used are maximum log-likehood (in BEKK and DVEC models) and twostep approach (in CCC model).

Keywords

• covariance
• multivariate GARCH models
• maximum likelihood estimation
• two-step estimation
• modeling