# Detecting nonlinear structure in time series

## Abstract

We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (United States)

- Sponsoring Org.:
- USDOE; DOHHS; USDOE, Washington, DC (United States); Department of Health and Human Services, Washington, DC (United States)

- OSTI Identifier:
- 5070920

- Report Number(s):
- LA-UR-91-3345; CONF-9110200-2

ON: DE92002461; CNN: 1-R01-MH47184-01; TRN: 91-032175

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: 1. experimental chaos conference, Arlington, VA (United States), 1-3 Oct 1991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; TIME-SERIES ANALYSIS; NONLINEAR PROBLEMS; RANDOMNESS; STATISTICS; MATHEMATICS; 990200* - Mathematics & Computers

### Citation Formats

```
Theiler, J.
```*Detecting nonlinear structure in time series*. United States: N. p., 1991.
Web.

```
Theiler, J.
```*Detecting nonlinear structure in time series*. United States.

```
Theiler, J. Tue .
"Detecting nonlinear structure in time series". United States. https://www.osti.gov/servlets/purl/5070920.
```

```
@article{osti_5070920,
```

title = {Detecting nonlinear structure in time series},

author = {Theiler, J},

abstractNote = {We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1991},

month = {1}

}