Extreme values of autocorrelated sequences

摘要

The extreme values of a sequence of autocorrelated random variables are examined. Specifically, the distribution function of the maximum value in a sequence of n autocorrelated random variables has been derived for the case where certain assumptions about the nature of the autocorrelation and about the distribution of the underlying random variables are made. These results also lead to the definition of an equivalent number of independent observations for estimating the maximum value of such a sequence. This parameter quantities the effective reduction in sample size, or number of observations, which occurs due to the autocorrelation. Selected moments of the distribution of the maximum value also are determined. Other results presented yield a method for calculating certain properties of interest about the maximum value in a dependent sequence (e.g., probabilities, mean, and variance) as a function of selected statistical descriptors of the underlying random variables, and the sample size.