Removing the Noise from Chaos Plus Noise

Steven P. Lalley

Chapter Chapter 9 in Nonlinear Dynamics and Statistics, 2001, pp 233-244 from Springer

Abstract: Abstract The problem of extracting a “signal” xn generated by a dynamical system from a time series yn = xn + en, where en is an observational error, is considered. It is shown that consistent signal extraction is impossible when the errors are distributed according to a density with unbounded support, and the underlying dynamical system admits bomoclinic pairs. It is also shown that consistent signal extraction is possible when the errors are uniformly bounded by a suitable constant and the underlying dynamical system has the “weak orbit separation property”. Simple algorithms for signal recovery are described in the latter case.

Keywords: Chaotic System; Hyperbolic System; Invariant Probability Measure; Sensitive Dependence; Smoothing Algorithm (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0177-9_9

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DOI: 10.1007/978-1-4612-0177-9_9

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