Determination of the noise level of chaotic time series

Abstract

We propose a method to determine the amount of measurement noise present in a chaotic time series. If the data are embedded in a space of higher dimension than that strictly required to reconstruct the dynamics, the extra dimensions are dominated by the noise, which results in a certain shape of the correlation integral. For the case in which only Gaussian noise is present, this shape can be calculated analytically as a function of the noise level. Thus the noise level can be obtained from a simple function fit. The analytical result also shows that a noise level of more than 2% will obscure any possible scaling of the correlation integral and thus makes it impossible to estimate the correlation dimension.