Extreme Values of Non-Stationary Sequences and the Extremal Index

摘要

The conditions used to generalize the extreme value theory for stationary random sequences to non-stationary sequences are studied with respect to their necessity. The authors find that the extremal index, defined in the stationary case, plays a similar role in the non-stationary case. The details show that this index describes not only the behavior of exceedances above a high level constant boundary, but also above a non-constant high level boundary.