Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 2000,80
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.
multivariate GARCH fourth moments kurtosis co-kurtosis impulse response function