Determining the minimum embedding dimensions of input-output time series data

Citation
Ly. Cao et al., Determining the minimum embedding dimensions of input-output time series data, INT J B CH, 8(7), 1998, pp. 1491-1504
Citations number
19
Categorie Soggetti
Multidisciplinary
Journal title
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN journal
02181274 → ACNP
Volume
8
Issue
7
Year of publication
1998
Pages
1491 - 1504
Database
ISI
SICI code
0218-1274(199807)8:7<1491:DTMEDO>2.0.ZU;2-X
Abstract
Input-output dynamical systems are in many ways quite different from the au tonomous systems that are usually modeled in dynamical system reconstructio n. In this paper we investigate the problem of determining the embedding di mension of such systems from input and output data. A successful embedding is essential if one wishes to model the system, or to design a control law. We propose a variant of the well-known false nearest neighbors method, whi ch we call the method of averaged false nearest neighbors. Our method has a simple interpretation and is easy to implement on a computer. We provide s everal numerical examples.