## On Selecting Models for Nonlinear Time Series (1995)

Venue: | Physica D |

Citations: | 52 - 14 self |

### BibTeX

@ARTICLE{Judd95onselecting,

author = {Kevin Judd and Alistair Mees},

title = {On Selecting Models for Nonlinear Time Series},

journal = {Physica D},

year = {1995},

volume = {82},

pages = {426--444}

}

### Years of Citing Articles

### OpenURL

### 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. 1 The Model Selection Problem As our understanding of chaotic and other nonlinear phenomena has grown, it has become apparent that linear models are inadequate to model most dynamical processes. Nevertheless, linear models...

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Citation Context ...cases. The difficulty illustrated by (15) is not an isolated example. On the contrary, it appears that finding the optimal model of size k is NP-hard---related to the feasible basis extension problem =-=[18, 5]-=----although we have not established this rigorously. If this is the case, then we cannot expect to obtain the optimal solution easily. On the other hand, numerical tests with real time series suggest ... |

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