GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION

This paper develops a generalized autoregressive conditional correlation ~GARCC! model when the standardized residuals follow a random coefficient vector autoregressive process+ As a multivariate generalization of the Tsay ~1987, Journal of the American Statistical Association 82, 590–604! random coefficient autoregressive ~RCA! model, the GARCC model provides a motivation for the conditional correlations to be time varying+ GARCC is also more general than the Engle ~2002, Journal of Business & Economic Statistics 20, 339–350! dynamic conditional correlation ~DCC! and the Tse and Tsui ~2002, Journal of Business & Economic Statistics 20, 351–362! varying conditional correlation ~VCC! models and does not impose unduly restrictive conditions on the parameters of the DCC model+ The structural properties of the GARCC model, specifically, the analytical forms of the regularity conditions, are derived, and the asymptotic theory is established+ The Baba, Engle, Kraft, and Kroner ~BEKK! model of Engle and Kroner ~1995, Econometric Theory 11, 122–150! is demonstrated to be a special case of a multivariate RCA process+ A likelihood ratio test is proposed for several special cases