Correlation integral as a tool for distinguishing between dynamics and statistics in time series data
type: Item
instance of: scholarly article
title: Correlation integral as a tool for distinguishing between dynamics and statistics in time series data
zbMATH Open document ID: 0988.37097
DOI: 10.1016/S0167-2789(98)00093-1
published in: Physica D
publication date: 2000-02-06T00:00:00Z
review text: The authors propose a simple criterion for time series analysis which is based on the correlation integral. They consider the following classes of data: (a) data from smooth low-dimensional dynamical systems, (b) data from high-dimensional systems, (c) data from deterministic but nonsmooth systems, (d) stationary random processes, (e) nonstationary processes. Note that in most cases the correlation integral is a good tool, since its calculation usually requires less data points than many others.
Mathematics Subject Classification ID: 37M10
Mathematics Subject Classification ID: 37H10
zbMATH DE Number: 1399218
zbMATH Keywords: high-dimensional system
zbMATH Keywords: stationary random process
zbMATH Keywords: time series analysis
zbMATH Keywords: correlation integral
author: Alexei B. Potapov
author: J. Kurths
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Time series and dependent variables
cites work: Dependent variables in broad band continuous time series
cites work: Statistical tests for deterministic effects in broad band time series
cites work: Measuring the strangeness of strange attractors
cites work: Ergodic theory of chaos and strange attractors
cites work: An attractor in a solar time series
cites work: Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
cites work: Q3658782
cites work: Embedology
cites work: Estimating correlation dimension from a chaotic time series: When does plateau onset occur?
cites work: State space reconstruction in the presence of noise
cites work: The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fiction
cites work: Independence in time series: another look at the BDS test
cites work: The statistical properties of dimension calculations using small data sets
cites work: Q3838898
cites work: Improvement of \(K_ 2\)-entropy calculations by means of dimension scaled distances
full work available at URL: s0167-2789(98)00093-1
OpenAlex ID: W2056706229
description: scientific article; zbMATH DE number 1399218