Sequential monitoring of the tail behavior of dependent data

•A sequential monitoring procedure for the tail behavior of time series is proposed.•An algorithm using extreme quantile estimates performs well in simulations.•Stock returns exhibit extremal instability during the recent crisis of 2007-2008.

We construct a sequential monitoring procedure for changes in the tail index and extreme quantiles of β-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.