The analysis of correlation integrals in terms of extremal value theory

In this paper we first give an overview of the methods of analysis of time series in terms of correlation integrals, which were developed for time series generated by deterministic systems. From the extremal value theory one obtains asymptotic information on the behaviour of the correlation integrals of time series generated by non-deterministic (mixing) systems. This leads to an analysis in terms of correlation integrals which is complementary to the estimation of dimension and entropy.Dedicated to the memory of Ricardo Mañé