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Detecting determinism in univariate and multivariate time series is difficult if the underlying process is nonlinear, and the noise level is high. In a previous paper, the authors proposed a method based on observable ordinal patterns. This method exploits the robustness of admissible ordinal patterns against observational noise, and the super-exponential growth of forbidden ordinal patterns with the length of the patterns. The new method compared favorably to the Brock-Dechert-Scheinkman independence test when applied to time series projected from the Hénon attractor and contaminated with Gaussian noise of different variances. In this paper, we extend this comparison to higher fractal dimensions by using noisy orbits on the attractors of the Lorenz map, and the time-delayed Hénon map. Finally, we make an analysis that enlightens the robustness of admissible ordinal patterns in the presence of observational noise. [ABSTRACT FROM AUTHOR]

We have proposed an adaptive procedure in order to estimate unknown parameters of a numerical model of a chaotic CO2 laser, which is observed through a time series that represents the output intensity of the laser. To do that, we consider a coupled system with the same functional form and adjustable parameters. The salient feature of the proposed technique is that accurate parameter estimation and identical synchronization can be jointly achieved by adaptively adjusting the desired parameters of the coupled system. [ABSTRACT FROM AUTHOR]