- Published 2012

In this work we extend the details of a linear least squares method to estimate the noise level in chaotic time series which has been previously proposed in [1]. For this purpose we analyze a non iterative algorithm based on the functional form obtained by Schreiber in 1993 where the effects of noise on L∞ norm correlation sums can be quantified via the nonlinear functional. The modified version of the functional leads to a linear approach that gives satisfactory results for simulated continuous flow data even for high level of noise contamination (up to 80%). The approach is especially useful to determine the effective fitting range of data. The range is limited by the curvature effects of the attractor and fluctuations in small scales. We also seek for a phenomenological model for the curvature effect depending on the empirical distribution of estimation errors.

@inproceedings{oban2012LinearLS,
title={Linear Least Squares Estimate of Noise Level in Chaotic Time Series via L∞ Norm Correlation Sum},
author={G{\"{u}rsan Çoban and Ali H. B{\"{u}y{\"{u}kl{\"{u} and Atin Das},
year={2012}
}