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Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility

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  • Michael McAleer
  • Suhejla Hoti
  • Felix Chan

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.

Suggested Citation

  • Michael McAleer & Suhejla Hoti & Felix Chan, 2009. "Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 422-440.
  • Handle: RePEc:taf:emetrv:v:28:y:2009:i:5:p:422-440
    DOI: 10.1080/07474930802467217
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