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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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Bibliographic Info

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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  1. 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.
  2. Rose, A.K. & Svensson, L.E.O., 1993. "European Exchange Rate Credibility Before the Fall," Papers 542, Stockholm - International Economic Studies.
  3. HAFNER, Christian M. & HERWARTZ, Helmut, 1998. "Volatility impulse response functions for multivariate GARCH models," CORE Discussion Papers 1998047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
  5. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  6. 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).
  7. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  8. Hafner, Christian M. & Herwartz, Helmut, 1998. "Testing for linear autoregressive dynamics under heteroskedasticity," SFB 373 Discussion Papers 1999,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  9. 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.
  10. repec:wop:humbsf:1998-41 is not listed on IDEAS
  11. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-72561, Tilburg University.
  12. 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.
  13. 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..
  14. 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.
  15. 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.
  16. 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.
  17. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  18. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
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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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