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Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series $\mb{Y}_n$, ${n\geq 1}$, rescaled through random factors $\mb{T}_n$, ${n\geq 1}$, extending some scale mixture models in the literature. We analyze its extremal behavior by deriving the maximum domain of attraction and the multivariate extremal index, which leads to new ways to construct multivariate extreme value distributions. The computation of the multivariate extremal index and the characterization of the tail dependence show the interesting property of these models that however much it is the dependence within and between factors $\mb{T}_n$, ${n\geq 1}$, the extremal index of the model is unit whenever $\mb{Y}_n$, ${n\geq 1}$, presents cross-sectional and sequencial tail independence. We illustrate with examples of thinned multivariate time series and multivariate autoregressive processes with random coefficients. An application of these latter to financial data is presented at the end.

We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we derive a new method of construction of multivariate extreme value copulas. We characterize the extremal dependence by computing the multivariate extremal index and bivariate upper tail dependence coefficients. An estimation procedure for the multivariate extremal index shall be presented. We also address the marginal estimation and propose a new estimator for the ARMAX autoregressive parameter.

The well-known M4 processes of Smith and Weissman are very flexible models for asymptotically dependent multivariate data. Extended M4 of Heffernan \emph{et al.} allows to also account for asymptotic independence. In this paper we introduce a more general multivariate model comprising asymptotic dependence and independence, which has the extended M4 class as a particular case. We study properties of the proposed model. In particular, we compute the multivariate extremal index, tail dependence and extremal coefficients.

Financial crises are a recurrent phenomenon with important effects on the real economy. The financial system is inherently fragile and it is therefore of great importance to be able to measure and characterize its systemic stability. Multivariate extreme value theory provide us such a framework through the \emph{fragility index} (Geluk \cite{gel+}, \emph{et al.}, 2007; Falk and Tichy, \cite{falk+tichy1,falk+tichy2} 2010, 2011). Here we generalize this concept and contribute to the modeling of the stability of a stochastic system divided into blocks. We will find several relations with well-known tail dependence measures in literature, which will provide us immediate estimators. We end with an application to financial data.

Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss events. A common measure of tail dependence is given by the so-called tail-dependence coefficient. We present a simple estimator of this latter that avoids the drawbacks of the estimation procedure that has been used so far. We prove strong consistency and asymptotic normality and analyze the finite sample behavior through simulation. We illustrate with an application to financial data.

The Gumbel max-domain of attraction corresponds to a null tail index which do not distinguish the different tail weights that might exist between distributions within this class. The Weibull-type distributions form an important subgroup of this latter and includes the so-called \emph{Weibull-tail coefficient}, usually denoted \theta, that specifies the tail behavior, with larger values indicating slower tail decay. Here we shall see that the Weibull-type distributions present a penultimate tail behavior Fr\'echet if \theta>1 and a penultimate tail behavior Weibull whenever \theta<1.

Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to assess the amount of dependence in $d$-variate random vectors based on bidimensional techniques. Very simple estimators will be stated and can be applied to the well-known \emph{stable tail dependence function}. Asymptotic normality and strong consistency will be derived too. An application to financial markets will be presented at the end.