{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:39:25Z","timestamp":1772293165717,"version":"3.50.1"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:p>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\u2013Dechert\u2013Scheinkman independence test when applied to time series projected from the H\u00e9non 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 H\u00e9non map. Finally, we make an analysis that enlightens the robustness of admissible ordinal patterns in the presence of observational noise.<\/jats:p>","DOI":"10.1142\/s0218127410027453","type":"journal-article","created":{"date-parts":[[2010,10,14]],"date-time":"2010-10-14T09:30:22Z","timestamp":1287048622000},"page":"2915-2924","source":"Crossref","is-referenced-by-count":31,"title":["DETECTING DETERMINISM IN TIME SERIES WITH ORDINAL PATTERNS: A COMPARATIVE STUDY"],"prefix":"10.1142","volume":"20","author":[{"given":"J. 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