A linearization based non-iterative approach to measure the gaussian noise level for chaotic time series

In this work we propose a non-iterative method to determine the noise level of chaotic time series. For this purpose, we use the gaussian noise functional derived by Schreiber in 1993. It is shown that the noise function could be approximated by a stretched exponential decay form. The decay function is then used to construct a linear least squares approach where global solution exists. We have developed a software basis to calculate the noise level which is based on TISEAN algorithms. A practical way to exclude the outlying observations for small length scales has been proposed to prevent estimation bias. The algorithm is tested on well known chaotic systems including Henon, Ikeda map and Lorenz, Rössler, Chua flow data. Although the results of the algorithm obtained from simulated discrete dynamics are not satisfactory, we have shown that it performs well on flow data even for extreme level of noise. The results that are obtained from the real world financial and biomedical time series have been interpreted.

► Noise level of time series can be estimated linearly from L∞ norm correlation sums.
► Schreiber’s nonlinear approach gives better estimates for flow data, and can be applied on extreme noise levels.
► The derived linear method can be used automatically for stream data.
► The fitting procedure is nearly 300 times faster than the existing nonlinear procedure.