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Fourth moments of multivariate GARCH processes

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  • HAFNER, Christian

Abstract

This paper 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 co-kurtosis between components. Applications of the results include the definition of impulse response functions for kurtosis and co-kurtosis, the derivation of the spectral density matrix of the squares and crossproducts, and a measure for causality in volatility. A bivariate exchange rate example illustrates the applications.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2001046.

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Date of creation: 00 Jun 2001
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Handle: RePEc:cor:louvco:2001046

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Keywords: multivariate GARCH; fourth moments; kurtosis; co-kurtosis;

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References

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  1. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
  2. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
  3. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
  4. Drost, F.C. & Werker, B.J.M., 1994. "Closing the GARCH gap: Continuous time GARCH modeling," Discussion Paper 1994-2, Tilburg University, Center for Economic Research.
  5. Andrew K. Rose & Lars E.O. Svensson, 1993. "European Exchange Rate Credibility Before the Fall," NBER Working Papers 4495, National Bureau of Economic Research, Inc.
  6. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
  7. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
  8. BROZE, Laurence & FRANCQ , Christian & ZAKOIAN, Jean-Michel, . "Non-redundancy of high order moment conditions for efficient GMM estimation of weak AR processes," CORE Discussion Papers RP -1576, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  10. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
  11. Christian M. Hafner & Helmut Herwartz, 2000. "Testing for linear autoregressive dynamics under heteroskedasticity," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 177-197.
  12. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-44.
  13. HAFNER, Christian & HERWARTZ, Helmut, 2001. "Volatility impulse response functions for multivariate GARCH models," CORE Discussion Papers 2001039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  15. H. Herwartz, 1998. "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," SFB 373 Discussion Papers 1998,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  16. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
  17. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  18. repec:wop:humbsf:1998-41 is not listed on IDEAS
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Cited by:
  1. Schüler, Martin & Schröder, Michael, 2003. "Systemic Risk in European Banking: Evidence from Bivariate GARCH Models," ZEW Discussion Papers 03-11, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.

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