  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.
