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Consistent nonlinear dynamics: identifying model inadequacy

McSharry, Patrick E. and Smith, Leonard A. (2004) Consistent nonlinear dynamics: identifying model inadequacy. Physica D: Nonlinear Phenomena, 192 (1-2). pp. 1-22. ISSN 0167-2789

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Identification Number: 10.1016/j.physd.2004.01.003


Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional statistics of nonlinear models like root-mean-square (RMS) forecast error can prove misleading. Testing consistency is shown to overcome some of the deficiencies of RMS error, both within the perfect model scenario and when applied to data from several physical systems using previously published models. In particular, testing for consistent nonlinear dynamics provides insight towards (i) identifying when a delay reconstruction fails to be an embedding, (ii) allowing state-dependent model selection and (iii) optimising local neighbourhood size. It also provides a more relevant (state dependent) threshold for identifying false nearest neighbours.

Item Type: Article
Official URL:
Additional Information: © Elsevier 2004
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QC Physics
Date Deposited: 27 Jan 2009 13:43
Last Modified: 02 Jun 2024 04:27

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