Holger Kantz

Learn More
published by the press syndicate of the university of cambridge The publisher has used its best endeavours to ensure that the URLs for external websites referred to in this book are correct and active at the time of going to press. However, the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that(More)
The false nearest neighbor method introduced by Kennel et al. [Phys. Rev. A 45, 3403 (1992)] is revisited and modified in order to ensure a correct distinction between low-dimensional chaotic data and noise. Still, correlated noise processes can yield vanishing percentages of false nearest neighbors for rather low embedding dimensions and can be mistaken(More)
We analyze prediction schemes for stochastic time series data. We propose that under certain conditions, a scalar time series, obtained from a vector-valued Markov process can be modeled as a finite memory Markov process in the observable. The transition rules of the process are easily computed using simple nonlinear time series predictors originally(More)
We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy(More)
Intuitively, music has both predictable and unpredictable components. In this paper, we assess this qualitative statement in a quantitative way using common time series models fitted to state-of-the-art music descriptors. These descriptors cover different musical facets and are extracted from a large collection of real audio recordings comprising a variety(More)
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincaré recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence(More)
The reconstruction of Fokker-Planck equations from observed time series data suffers strongly from finite sampling rates. We show that previously published results are degraded considerably by such effects. We present correction terms which yield a robust estimation of the diffusion terms, together with a novel method for one-dimensional problems. We apply(More)
A local projective noise reduction scheme, originally developed for low-dimensional stationary deterministic chaotic signals, is successfully applied to human speech. This is possible by exploiting properties of the speech signal which resemble structure exhibited by deterministic dynamical systems. In high-dimensional embedding spaces, the strong inherent(More)