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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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    References 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 - 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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