Fourth Moment Structure of Multivariate GARCH Models

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Abstract
This article 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 cokurtosis between components. Applications of the results include the definition of impulse response functions for kurtosis and cokurtosis, the derivation of the spectral density matrix of the squares and cross products, and a measure for causality in volatility. A bivariate exchange rate example illustrates the applications.

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