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Fourth Moment Structure of Multivariate GARCH Models

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Author Info
Christian M. Hafner

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Abstract

This article derives conditions for the existence of fourth moments of multivariate GARCH processes in the general vector specification and gives explicit results for the fourth moments and autocovariances of the squares and cross products. Results are provided for the kurtosis and cokurtosis between components. Applications of the results include the definition of impulse response functions for kurtosis and cokurtosis, the derivation of the spectral density matrix of the squares and cross products, and a measure for causality in volatility. A bivariate exchange rate example illustrates the applications. , .

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Publisher Info
Article provided by Oxford University Press in its journal Journal of Financial Econometrics.

Volume (Year): 1 (2003)
Issue (Month): 1 ()
Pages: 26-54
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Handle: RePEc:oup:jfinec:v:1:y:2003:i:1:p:26-54

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  1. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  2. Christian Conrad & Menelaos Karanasos, 2008. "Negative Volatility Spillovers in the Unrestricted ECCC-GARCH Model," KOF Working papers 08-189, KOF Swiss Economic Institute, ETH Zurich. [Downloadable!]
  3. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Quantitative Analysis Unit Working Paper QAU08-4, Federal Reserve Bank of Boston. [Downloadable!]
  4. Peter Zadrozny, 2005. "Necessary and Sufficient Restrictions for Existence of a Unique Fourth Moment of a Univariate GARCH(p,q) Process," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  5. Hafner, Christian M. & Herwartz, Helmut, 2004. "Testing for Causality in Variance using Multivariate GARCH Models," Economics Working Papers 2004,03, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
    Other versions:
  6. E.Panopoulou & T. Pantelidis, 2005. "Integration at a cost: Evidence from volatility impulse response functions," Economics, Finance and Accounting Department Working Paper Series n1540305, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth. [Downloadable!]
    Other versions:
  7. Luc, BAUWENS & C.M., HAFNER & J.V.K., ROMBOUTS, 2006. "Multivariate mixed normal conditional heteroskedasticity," Discussion Papers (ECON - Département des Sciences Economiques) 2006007, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
    Other versions:
  8. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109. [Downloadable!]
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  9. HAFNER, Christian M. & PREMINGER, Arie, 2006. "Asymptotic theory for a factor GARCH model," CORE Discussion Papers 2006071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  10. Christian M. Hafner, 2004. "Temporal aggregation of multivariate GARCH processes," Econometric Society 2004 North American Winter Meetings 538, Econometric Society. [Downloadable!]
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  11. Andrea Silvestrini & David Veredas, 2008. "Temporal aggregation of univariate and multivariate time series models: A survey," Temi di discussione (Economic working papers) 685, Bank of Italy, Economic Research Department. [Downloadable!]
    Other versions:
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