Structural analysis of spatio-temporal threshold exceedances

Due to both the complexity of real systems and the technical difficulties inherent to extremal analysis, the statistics of extremes in spatio-temporal processes has become one of the most challenging research areas in relation to the increasingly demanding interest on risk assessment tools in many fields of application. Recent advances in spatio-temporal statistical analysis are focused, in particular, on the formulation and study of new model families, flexible to represent such real complexities and, at the same time, suitable for technical treatment and interpretation, as well as on related system dynamics problems. In this paper, significant characteristics of threshold exceedances with reference to structural properties of the processes generating such events, particularly in the context of input/output systems, are analyzed. Specifically, the effect of spatial deformation and blurring transformations on the second order structure and the geometrical properties of excursion sets is studied and illustrated through some simulated cases. A spatio-temporal model based on spatial deformation and blurring, which provides a suitable representation for a variety of environmental applications, is formulated, and further aspects regarding the temporal structure of threshold exceedances are explored and discussed. Copyright (C) 2009 John Wiley & Sons, Ltd.