On selecting models for nonlinear time series

Kevin Judd, A.I. Mees

Research output: Contribution to journalArticle

195 Citations (Scopus)

Abstract

Constructing models from time series with nontrivial dynamics involves the problem of how to choose the best model from within a class of models, or to choose between competing classes. This paper discusses a method of building nonlinear models of possibly chaotic systems from data, while maintaining good robustness against noise. The models that are built are close to the simplest possible according to a description length criterion. The method will deliver a linear model if that has shorter description length than a nonlinear model. We show how our models can be used for prediction, smoothing and interpolation in the usual way. We also show how to apply the results to identification of chaos by detecting the presence of homoclinic orbits directly from time series.
Original languageEnglish
Pages (from-to)426-444
JournalPhysica D
Volume82
Issue number4
DOIs
Publication statusPublished - 1995

Fingerprint

smoothing
interpolation
chaos
orbits
predictions

Cite this

Judd, Kevin ; Mees, A.I. / On selecting models for nonlinear time series. In: Physica D. 1995 ; Vol. 82, No. 4. pp. 426-444.
@article{35b8fc2b79ce4a5c80d86a49ce5fdc17,
title = "On selecting models for nonlinear time series",
abstract = "Constructing models from time series with nontrivial dynamics involves the problem of how to choose the best model from within a class of models, or to choose between competing classes. This paper discusses a method of building nonlinear models of possibly chaotic systems from data, while maintaining good robustness against noise. The models that are built are close to the simplest possible according to a description length criterion. The method will deliver a linear model if that has shorter description length than a nonlinear model. We show how our models can be used for prediction, smoothing and interpolation in the usual way. We also show how to apply the results to identification of chaos by detecting the presence of homoclinic orbits directly from time series.",
author = "Kevin Judd and A.I. Mees",
year = "1995",
doi = "10.1016/0167-2789(95)00050-E",
language = "English",
volume = "82",
pages = "426--444",
journal = "Physica D",
issn = "0167-2789",
publisher = "Pergamon",
number = "4",

}

On selecting models for nonlinear time series. / Judd, Kevin; Mees, A.I.

In: Physica D, Vol. 82, No. 4, 1995, p. 426-444.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On selecting models for nonlinear time series

AU - Judd, Kevin

AU - Mees, A.I.

PY - 1995

Y1 - 1995

N2 - Constructing models from time series with nontrivial dynamics involves the problem of how to choose the best model from within a class of models, or to choose between competing classes. This paper discusses a method of building nonlinear models of possibly chaotic systems from data, while maintaining good robustness against noise. The models that are built are close to the simplest possible according to a description length criterion. The method will deliver a linear model if that has shorter description length than a nonlinear model. We show how our models can be used for prediction, smoothing and interpolation in the usual way. We also show how to apply the results to identification of chaos by detecting the presence of homoclinic orbits directly from time series.

AB - Constructing models from time series with nontrivial dynamics involves the problem of how to choose the best model from within a class of models, or to choose between competing classes. This paper discusses a method of building nonlinear models of possibly chaotic systems from data, while maintaining good robustness against noise. The models that are built are close to the simplest possible according to a description length criterion. The method will deliver a linear model if that has shorter description length than a nonlinear model. We show how our models can be used for prediction, smoothing and interpolation in the usual way. We also show how to apply the results to identification of chaos by detecting the presence of homoclinic orbits directly from time series.

U2 - 10.1016/0167-2789(95)00050-E

DO - 10.1016/0167-2789(95)00050-E

M3 - Article

VL - 82

SP - 426

EP - 444

JO - Physica D

JF - Physica D

SN - 0167-2789

IS - 4

ER -