Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility

Abstract

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), 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.Asymmetric effects, Asymptotic theory, Conditional volatility, Multivariate structure, Regularity conditions,

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“…Therefore, taking account of the volatility transmission effects across different markets and assets (specifically, exchange rate returns and stock index returns), together with the asymmetric effect, this paper adopts the VARMA-AGARCH model originally proposed by Ling and McAleer (2003) and extended in McAleer et al (2009). This specification nests the univariate asymmetric GJR model of Glosten, Jagannathan and Runkle (1993) in modelling the conditional variance process.…”

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