Translation models and extremes

Abstract

Translation models are constructed for non-Gaussian random vectors, time series and continuous time processes. They are memoryless, monotonically increasing transformations of corresponding Gaussian elements. It is shown that, generally, extremes of target non-Gaussian elements cannot be approximated by those of their translation models. This limitation has two sources. First, translation models cannot characterize accurately uncorrelated but dependent random variables. Second, extremes of correlated Gaussian variables are asymptotically independent and so are the extremes of the translation models constructed on these variables. Examples are presented to illustrate these limitations of translation models.