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Fourth moments of multivariate GARCH processes

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  • Hafner, Christian M.

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. An impulse response function for kurtosis and co-kurtosis is defined that allows to analyse the expectation of the (co-)kurtosis conditional on an initial shock. For a bivariate exchange rate series, these functions indicate that there is a trade-off between conditional variance and conditional kurtosis: the conditional variance increases with the size of the shocks, hut the conditional kurtosis decreases.

Suggested Citation

  • Hafner, Christian M., 2000. "Fourth moments of multivariate GARCH processes," SFB 373 Discussion Papers 2000,80, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200080
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    1. Broze, Laurence & Francq, Christian & Zakoian, Jean-Michel, 2001. "Non-redundancy of high order moment conditions for efficient GMM estimation of weak AR processes," Economics Letters, Elsevier, vol. 71(3), pages 317-322, June.
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    4. C. M. Hafner & H. Herwartz, 1998. "Structural analysis of portfolio risk using beta impulse response functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(3), pages 336-355, November.
    5. 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..
    6. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    7. Christian M. Hafner & Helmut Herwartz, 2000. "Testing for linear autoregressive dynamics under heteroskedasticity," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 177-197.
    8. He, Changli & Teräsvirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(6), pages 824-846, December.
    9. 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.
    10. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
    11. Rose, Andrew K. & Svensson, Lars E. O., 1994. "European exchange rate credibility before the fall," European Economic Review, Elsevier, vol. 38(6), pages 1185-1216, June.
    12. 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.
    13. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    14. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-186, January.
    15. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-844.
    16. HAFNER, Christian & HERWARTZ, Helmut, 1998. "Volatility impulse response functions for multivariate GARCH models," LIDAM Discussion Papers CORE 1998047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Herwartz, H., 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.
    18. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    19. 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.
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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 - Leibniz Centre for European Economic Research.

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    More about this item

    Keywords

    multivariate GARCH; fourth moments; kurtosis; co-kurtosis; impulse response function;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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