Estimating multivariate volatility models equation by equation

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 78; no. 3; pp. 613 - 635
• Main Authors: Francq, Christian, Zakoïan, Jean-Michel
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.06.2016; John Wiley & Sons Ltd; Oxford University Press
• Subjects: Asymptotic properties; Consistency; Constant conditional correlation; Correlation; Dynamic conditional correlation; equations; Estimating; Estimators; heteroskedasticity; Mathematical analysis; Mathematical models; Monte Carlo method; Monte Carlo simulation; Multivariate generalized auto-regressive conditional heteroscedasticity specification testing; Quasi-maximum-likelihood estimation; Statistical analysis; Statistical methods; Statistics; Studies; Volatility
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/rssb.12126

The paper investigates the estimation of a wide class of multivariate volatility models. Instead of estimating an m-multivariate volatility model, a much simpler and numerically efficient method consists in estimating m univariate generalized auto-regressive conditional heteroscedasticity type models equation by equation in the first step, and a correlation matrix in the second step. Strong consistency and asymptotic normality of the equation-by-equation estimator are established in a very general framework, including dynamic conditional correlation models. The equation-by-equation estimator can be used to test the restrictions imposed by a particular multivariate generalized auto-regressive conditional heteroscedasticity specification. For general constant conditional correlation models, we obtain the consistency and asymptotic normality of the two-step estimator. Comparisons with the global method, in which the model parameters are estimated in one step, are provided. Monte Carlo experiments and applications to financial series illustrate the interest of the approach.