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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.

Suggested Citation

  • HAFNER, Christian, 2001. "Fourth moments of multivariate GARCH processes," LIDAM Discussion Papers CORE 2001046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2001046
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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;
    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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