Thresholds, news impact surfaces and dynamic asymmetric multivariate GARCH

• Published in: Statistica Neerlandica Vol. 65; no. 2; pp. 125 - 163
• Main Authors: Caporin, Massimiliano, McAleer, Michael
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.05.2011; Netherlands Society for Statistics and Operations Research
• Series: Statistica Neerlandica
• Subjects: Asymmetry; Asymptotic properties; asymptotic theory; conditional variance; Density; Dynamics; Mathematical analysis; Mathematical models; Multivariate analysis; multivariate asymmetry; multivariate news impact curve; News; stationarity conditions; Statistical analysis; Studies; Thresholds
• ISSN: 0039-0402; 1467-9574
• DOI: 10.1111/j.1467-9574.2010.00479.x

Dynamic Asymmetric Multivariate GARCH (DAMGARCH) is a new model that extends the Vector ARMA‐GARCH (VARMA‐GARCH) model of Ling and McAleer (2003) by introducing multiple thresholds and time‐dependent structure in the asymmetry of the conditional variances. Analytical expressions for the news impact surface implied by the new model are also presented. DAMGARCH models the shocks affecting the conditional variances on the basis of an underlying multivariate distribution. It is possible to model explicitly asset‐specific shocks and common innovations by partitioning the multivariate density support. This article presents the model structure, describes the implementation issues, and provides the conditions for the existence of a unique stationary solution, and for consistency and asymptotic normality of the quasi‐maximum likelihood estimators. The article also presents an empirical example to highlight the usefulness of the new model.