The stopped clock model

The extreme value theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological advances allowing an increasingly larger and more efficient data collection, there are sometimes failures in the records, which causes difficulties in statistical inference, especially in the tail where data are scarcer. In this article, we present a model with a simple and intuitive failures scheme, where each record failure is replaced by the last record available. We will study its extremal behavior with regard to local dependence and high values clustering, as well as the temporal dependence on the tail.

Automated summary

The extreme value theory provides specific tools for modeling and predicting extreme phenomena, with risk assessment commonly analyzed through measures for tail dependence and high values clustering. Despite advancements in data collection technology, failures in records can still cause difficulties in statistical inference, especially in the scarce data tail. In this article, a model with a simple and intuitive failures scheme is presented, where each record failure is replaced by the last available record. The extremal behavior of the model with respect to local dependence, high values clustering, and temporal dependence on the tail is studied.