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Identification of nonlinear time series via kernels

Identification of nonlinear time series via kernels
Identification of nonlinear time series via kernels
Given a time series arising as the observations of some dynamical system, it is possible to reconstruct the qualitative behaviour of the dynamical system. Given such a reconstruction, this provides a general approach for making accurate short-term predictions. The time series reconstruction problem can be viewed as a function approximation problem which can be addressed by reproducing kernel Hilbert spaces (RKHS). Such an approach is described and related to Bayesian estimation with Gaussian priors. It is also shown that an explicit formulation of the model as an input-dependent autoregressive model is possible. This linearization is, however, unlike other approaches, exact and the autoregressive coefficients can be calculated explicitly at each time step. A particular example of RKHS approximation is applied to two benchmark problems, one synthetic and one real. The results demonstrate various aspects related to the optimization of the models and also show that the RKHS method is competitive against the best alternatives.
737-750
Dodd, T.J.
a03ae08d-dd77-461e-a953-e52eec9d2dcc
Harris, C.J.
c4fd3763-7b3f-4db1-9ca3-5501080f797a
Dodd, T.J.
a03ae08d-dd77-461e-a953-e52eec9d2dcc
Harris, C.J.
c4fd3763-7b3f-4db1-9ca3-5501080f797a

Dodd, T.J. and Harris, C.J. (2002) Identification of nonlinear time series via kernels. Internation Journal of Systems Science, 33 (9), 737-750. (doi:10.1080/00207720210147070).

Record type: Article

Abstract

Given a time series arising as the observations of some dynamical system, it is possible to reconstruct the qualitative behaviour of the dynamical system. Given such a reconstruction, this provides a general approach for making accurate short-term predictions. The time series reconstruction problem can be viewed as a function approximation problem which can be addressed by reproducing kernel Hilbert spaces (RKHS). Such an approach is described and related to Bayesian estimation with Gaussian priors. It is also shown that an explicit formulation of the model as an input-dependent autoregressive model is possible. This linearization is, however, unlike other approaches, exact and the autoregressive coefficients can be calculated explicitly at each time step. A particular example of RKHS approximation is applied to two benchmark problems, one synthetic and one real. The results demonstrate various aspects related to the optimization of the models and also show that the RKHS method is competitive against the best alternatives.

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Published date: July 2002
Organisations: Southampton Wireless Group

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Local EPrints ID: 258875
URI: http://eprints.soton.ac.uk/id/eprint/258875
PURE UUID: 93d17b4f-875f-48fe-a8f5-10ed55ddfc0c

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Date deposited: 23 Feb 2004
Last modified: 29 Jan 2020 15:33

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Contributors

Author: T.J. Dodd
Author: C.J. Harris

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