Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility
扩展了单变量非对称GJR模型，提出常条件相关VARMA-非对称GARCH模型，建立其平稳性、因果展开和矩存在条件，并在非正态冲击下给出拟极大似然估计量的一致性和渐近正态性条件。
Various univariate and multivariate models of volatility have been used to evaluate market risk, asymmetric shocks, thresholds, leverage effects, and Value-at-Risk in economics and finance. This article is concerned with market risk, and develops a constant conditional correlation vector ARMA–asymmetric GARCH (VARMA–AGARCH) model, as an extension of the widely used univariate asymmetric (or threshold) GJR model of Glosten et al. (1992 Glosten , L. , Jagannathan , R. , Runkle , D. ( 1992 ). On the relation between the expected value and volatility of nominal excess return on stocks . Journal of Finance 46 : 1779 – 1801 . [Google Scholar]), and establishes its underlying structure, including the unique, strictly stationary, and ergodic solution of the model, its causal expansion, and convenient sufficient conditions for the existence of moments. Alternative empirically verifiable sufficient conditions for the consistency and asymptotic normality of the quasi-maximum likelihood estimator are established under non-normality of the standardized shocks.