11. Multivariate ARCH Models

  1. Evdokia Xekalaki and
  2. Stavros Degiannakis

Published Online: 31 MAR 2010

DOI: 10.1002/9780470688014.ch11

ARCH Models for Financial Applications

ARCH Models for Financial Applications

How to Cite

Xekalaki, E. and Degiannakis, S. (2010) Multivariate ARCH Models, in ARCH Models for Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470688014.ch11

Author Information

  1. Department of Statistics Athens University of Economics and Business, Greece

Publication History

  1. Published Online: 31 MAR 2010
  2. Published Print: 16 APR 2010

ISBN Information

Print ISBN: 9780470066300

Online ISBN: 9780470688014



  • maximum likelihood estimation;
  • multivariate ARCH models;
  • symmetric model specifications;
  • univariate ARCH models


The generalization of univariate models to a multivariate context leads to a straightforward application of ARCH models to portfolio selection and asset pricing theory. A number of models in the financial literature have dealt with imposing constraints in multivariate ARCH models in order to reduce the number of parameters to be estimated. These constraints have to be compatible with a positive definite conditional covariance matrix and must lead to tractable estimation procedures. As for the univariate ARCH models, the method of maximum likelihood can be applied to jointly estimate the parameters of the mean and the variance equations. In EViews 6 the estimation of multivariate ARCH models is available as a built-in system object. The multivariate models can be estimated via the rolling menus. EViews 6 allows the estimation of the Diag-BEKK, Diag-VECH and CCC-GARCH model specifications, assuming multivariate normal or multivariate Student t distributed innovations.

Controlled Vocabulary Terms

autoregressive conditional heteroskedasticity; maximum likelihood estimation; student's t-distribution