12. Multivariate GARCH

  1. Ngai Hang Chan

Published Online: 28 JAN 2011

DOI: 10.1002/9781118032466.ch12

Time Series: Applications to Finance with R and S-Plus, Second Edition

Time Series: Applications to Finance with R and S-Plus, Second Edition

How to Cite

Chan, N. H. (2010) Multivariate GARCH, in Time Series: Applications to Finance with R and S-Plus, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032466.ch12

Author Information

  1. The Chinese University of Hong Kong, Department of Statistics, Shatin, Hong Kong

Publication History

  1. Published Online: 28 JAN 2011
  2. Published Print: 13 SEP 2010

ISBN Information

Print ISBN: 9780470583623

Online ISBN: 9781118032466

SEARCH

Keywords:

  • BEKK model;
  • constant-correlation model;
  • multivariate GARCH model;
  • SAS;
  • single-factor GARCH model;
  • SPLUS

Summary

This chapter talks about a multivariate GARCH(1,1) model with k=3. It briefly discusses the general models: diagonal form and alternative matrix form. Due to the high-dimensional nature of the problem, multivariate GARCH models becomes inevitable that many of the models used in fitting multivariate GARCH series possess a rather complicated form. The examples given in the chapter enables the readers to acquire the essentials of fitting some commonly used multivariate GARCH models. The chapter briefly describes the two commonly used software products that support multivariate GARCH models: SPLUS and SAS. It also discusses quadratic form or BEKK model and its special case single-factor GARCH model and constant-correlation model. The chapter presents an example of foreign exchange rates used in Diebold and Nerlove. It is a rule rather than an exception that users must develop their own software support for fitting multivariate GARCH series.

Controlled Vocabulary Terms

correlation; foreign exchange rates; GARCH model; multivariate models