Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

Details Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

1999-11-30

arxiv.org/abs/chao-dyn/9912002v1

Phys. Rev. Lett. 83(21), 4285-4288, (1999)

Nonlinear Sciences

Chaotic Dynamics

RevTex, 11 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.83.4285

A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors even if the noise is IND. A new cost function is obtained via the maximum likelihood principle; superior results are illustrated both for small data sets and infinitely long data streams.

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