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Positivity Conditions for a Bivariate Autoregressive Volatility Specification

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  • C. Gourieroux

Abstract

We derive necessary and sufficient conditions for the positive definiteness of the predicted volatility matrix in a bivariate autoregressive volatility specification. These nonlinear inequality restrictions have strong implications in terms of causality between volatilities and covolatilities. Copyright , Oxford University Press.

Suggested Citation

  • C. Gourieroux, 2007. "Positivity Conditions for a Bivariate Autoregressive Volatility Specification," Journal of Financial Econometrics, Oxford University Press, vol. 5(4), pages 624-636, Fall.
    • Handle: RePEc:oup:jfinec:v:5:y:2007:i:4:p:624-636
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbm010
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    Cited by:

    1. Karanasos, Menelaos & Xu, Yongdeng & Yfanti, Stavroula, 2017. "Constrained QML Estimation for Multivariate Asymmetric MEM with Spillovers: The Practicality of Matrix Inequalities," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    2. Nakatani, Tomoaki & Teräsvirta, Timo, 2008. "Positivity constraints on the conditional variances in the family of conditional correlation GARCH models," Finance Research Letters, Elsevier, vol. 5(2), pages 88-95, June.
    3. Conrad, Christian & Karanasos, Menelaos, 2010. "Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 838-862, June.
    4. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.

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