Asymptotic Theory for General Multivariate GARCH Models

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Weibin Jiang*+ and Hao Yu and Reg Kulperger
• Companies: The University of Western Ontario and The University of Western Ontario and The University of Western Ontario
• Keywords: Multivariate GARCH ; QMLE ; Identifiability ; Ergodicity ; Strong Consistency ; Asymptotic Normality

Abstract

Generalized autoregressive conditional heteroscedasticity (GARCH) models are widely used in financial markets. Parameters of GARCH models are usually estimated by the quasi-maximum likelihood estimator (QMLE). In recent years, economic theory often implies equilibrium between the levels of time series, which makes the application of multivariate models a necessity. Unfortunately the asymptotic theory of the multivariate GARCH models is far from coherent since many algorithms on the univariate case do not extend to multivariate models naturally. This paper studies the asymptotic theory of the QMLE under mild conditions. We give some counterexamples for the parameter identifiability result in Jeantheau (1998) and provides a better necessary and sufficient condition. We prove the ergodicity of the conditional variance process on an application of theorems by Meyn and Tweedie (2009). Under those conditions, the consistency and asymptotic normality of the QMLE can be proved by the standard compactness argument and Taylor expansion of the logarithm of the score function.