Extremes of Non-stationary Sequences

Abstract

Non-stationary processes have characteristics that change systematically thorough time. In the context of environmental processes, non-stationarity is often apparent because of seasonal effects, perhaps due to different climate patterns in different months, or in the form of trends, possibly due to long-term climate changes. Like the presence of temporal dependence, such departures from the simple assumptions that were made in the derivation of the extreme value characterizations in Chapters 3 and 4 challenge the utility of the standard models. In Chapter 5 we were able to demonstrate that, in a certain sense and subject to specified limitations, the usual extreme value limit models are still applicable in the presence of temporal dependence. No such general theory can be established for non-stationary processes. Results are available for some very specialized forms of non-stationarity, but these are generally too restrictive to be of use for describing the patterns of non-stationarity found in real processes. Instead, it is usual to adopt a pragmatic approach of using the standard extreme value models as basic templates that can be enhanced by statistical modeling.