Sequential monitoring of the tail behavior of dependent data

Abstract

We construct a sequential monitoring procedure for changes in the tail index and extreme quantiles of ß-mixing random variables, which can be based on a large class of tail index estimators. The assumptions on the data are general enough to be satisfied in a wide range of applications. In a simulation study empirical sizes and power of the proposed tests are studied for linear and non-linear time series. Finally, we use our results to monitor Bank of America stock log-losses from 2007 to 2012 and detect changes in extreme quantiles without an accompanying detection of a tail index break.