THE EXTREMAL INDEX AND CLUSTERING OF HIGH VALUES FOR DERIVED STATIONARY-SEQUENCES

Given a sequence of independent identically distributed random variabl es, we derive a moving-maximum sequence (with random translations). Th e extremal index of the derived sequence is computed and the limiting behaviour of clusters of high values is studied. We are then given two or more independent stationary sequences whose extremal indices are k nown. We derive a new stationary sequence by taking either a pointwise maximum or by a mixture of the original sequences. In each case, we c ompute the extremal index of the derived sequence.