Fourth Moments of Multivariate Garch Processes
نویسنده
چکیده
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.
منابع مشابه
Properties and Estimation of GARCH(1,1) Model
We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-taile...
متن کاملNormal Mixture Garch(1,1): Applications to Exchange Rate Modelling
Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling ...
متن کاملBreak Detection in the Covariance Structure of Multivariate Time Series Models1 by Alexander Aue,
In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it ...
متن کاملBreak Detection in the Covariance Structure of Multivariate Time Series Models∗ by Alexander Aue
In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature and also works well in the case of high dimensionality of the underlying data. Since it i...
متن کامل