GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION

This paper develops a generalized autoregressive conditional correlation (GARCC) model when the standardized residuals follow a random coefficient vector auto-regressive 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 he 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 foms 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