A simple multivariate ARCH model specified by random coefficients

P.W. FONG, Wai Keung LI, Hong-Zhi AN

Research output: Contribution to journalArticle

7 Citations (Scopus)


This paper provides an alternative formulation of the conditional correlation structure in fitting the multivariate GARCH model. A special case is the multivariate ARCH model with random coefficients. Its coherence structure is derived by the correlations between the random coefficients which play an important role in describing the interested heteroscedastic features. The parameter estimation problem can be solved by maximum likelihood estimation and model selection is via the likelihood ratio test. We consider three real applications: (1) the spot and forward rates of the Deutsche Mark against the US dollars; (2) exchange rates of Deutsche Mark and Japanese Yen against US dollars; (3) the Heng Sang index and SES index. Copyright © 2005 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)1779-1802
JournalComputational Statistics and Data Analysis
Issue number3
Publication statusPublished - Dec 2006


Autoregressive Conditional Heteroscedasticity
Random Coefficients
Multivariate Models
Multivariate GARCH
Correlation Structure
Exchange rate
Likelihood Ratio Test
Maximum Likelihood Estimation
Model Selection
Parameter Estimation
Maximum likelihood estimation
Parameter estimation


Fong, P. W., Li, W. K., & An, H.-Z. (2006). A simple multivariate ARCH model specified by random coefficients. Computational Statistics and Data Analysis, 51(3), 1779-1802. doi: 10.1016/j.csda.2005.11.019


  • Likelihood ratio test
  • Maximum likelihood estimation
  • Multivariate autoregressive conditional heteroscedasticity
  • Nonconstant correlation
  • Random coefficient model
  • Hadamard product
  • Star product