Extremal clustering in non-stationary random sequences

Abstract It is well known that the distribution of extreme values strictly stationary sequences differ from those independent and identically distributed in extremal clustering may occur. Here we consider non-stationary but random variables subject to suitable long range dependence restrictions. We find limiting appropriately normalized sample maxima depends on a parameter measures average sequence. Based this new representation derive asymptotic for time between consecutive observations construct moment likelihood based estimators clustering. specialize our results with periodic structure.