Peter Hall & Liang Peng, Australian National University
Qiwei Yao, University of Kent at Canterbury
Abstract
We suggest moving-maximum models, based on weighted maxima of independent random variables, for extreme values from a time series. The models are particularly tractable, both analytically and numerically, and so are readily used in conjunction with bootstrap methods. In particular they lead to simple bootstrap techniques for constructing confidence and prediction intervals from dependent extrema. Importantly, the models address a wide range of stochastic processes that are of direct practical interest in the context of extreme-value data. For example, it is shown that a stationary stochastic process whose finite-dimensional distributions are extreme-value distributions may be approximated arbitrarily closely by a moving-maximum process with extreme-value marginals. Moreover, bootstrapped moving-maximum models may be used to capture the dominant features of a range of processes that are not themselves moving maxima. Methods for inference in moving-maximum models are discussed. Connections of moving-maximum models to more conventional, moving-average processes are noted, and their practical implications addressed.