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Nonlinear time-series analysis

A measurable variable of a system, observed continuously, may be regarded as an information signal. Sampling this signal, either on a time or event basis, and recording the measured values sequentually produces a discrete signal, or time series. For instance, atmospheric pressure may vary continuously throughout the day, but recording the pressure hourly would yield a time series.

The process of analyzing time series using mathematical and numerical data transformations or even appropriate graphical displays constitutes a field of science known as time-series analysis. Conventional signal-processing techniques include Fourier transforms, autocorrelation functions and autoregressive data modeling, but these methods generally rely on linear relations and often have been found insensitive in describing the nonlinear structure in chaotic time series.

Chaotic time-series analysis (CTSA), or nonlinear time-series analysis (NTSA), refers to a class of data-analysis techniques employed to provide a richer description of chaotic time series. The CRG has been involved continuously in developing and applying new CTSA algorithms to time series, and current research topics include stationarity tests, dynamical state classification and periodic orbit detection.

Recently (1996.5 - 2000.25), we have focused on the use of symbol-sequence statistics (derived from symbolic dynamics) to identify patterns in data hidden amidst high levels of dynamical and observational noise. The objective is to develop a set of tools for symbolic time-series analysis.

We have compiled a "Bibliography of symbolic time-series analysis" to assist in further research. The bibliography is by no means complete, and inclusion on this list is the prejudiced and subjective judgment of the list maintainer.

Primary contacts for this research area are: C.S. Daw, C.E.A. Finney and M.B. Kennel.

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Copyright © 1996-2002 C.E.A. Finney. Unless specified, use in any medium of any contents at this site is permitted, provided the source URL be acknowledged and the copyright notice be included. This page's URL is http://www-chaos.engr.utk.edu/res/ctsa.html.

Updated: 2001-12-27 ceaf