A new multivariate heavy-tailed distribution is proposed as an extension of the univariate distribution of Politis (2004). The properties of the new distribution are discussed, as well as its effectiveness in modeling ARCH/GARCH residuals. A practical procedure for multiparameter numerical maximum likelihood is also given, and a real data example is worked out. JEL codes: C3; C5.

This paper derives an analytical expression for an impulse-response function for a vector autoregression with multivariate GARCH errors, where the vector of conditional means is a function of the conditional variances. We also provide the appropriate interpretation of an impulse-response function for such models and suggest interesting empirical issues that can be addressed within this framework.

Generative moment matching networks (GMMNs) are introduced as dependence models for the joint innovation distribution of multivariate time series (MTS). Following popular copula–GARCH approach modeling dependent MTS data, a framework based on GMMN–GARCH is presented. First, ARMA–GARCH utilized to capture serial within each univariate marginal series. Second, if number large, principal component...

A methodology is presented for clustering financial time series in extreme scenario. The procedure is based on the calculation of some suitable pairwise conditional Spearman’s correlation coefficients. It does not assume any parametric model describing the time series under investigation, but only relies on the assumption that they follows a multivariate copula-GARCH model.

Instead of modeling asset price and currency risks separately, this paper derives the international hedge portfolio, hedging asset price and currency risk simultaneously for estimating the dynamic international optimal hedge ratio. The model estimation is specified in a multivariate GARCH setting with vector error correction terms and estimated for the commodity and stock markets of the U.S., t...

A multivariate extension of the exponential continuous time GARCH(p, q) model (ECOGARCH) is introduced and studied. Stationarity and mixing properties of the new stochastic volatility model are investigated and ways to model a component-wise leverage effect are presented. AMS Subject Classification 2000: Primary: 60G51; 60H10 Secondary: 91B72; 91B84

This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standard...

This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications, the inference methods, and identifies likely directions of future research.

The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the “curse of dimensionality”. For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parame...