Probabilistic divergence of permutations for nonlinearity detection

Abstract To detect the nonlinearity of complex time series, we propose a novel method by measuring the probabilistic divergence of permutations (PDP), and we apply the division-based relative entropy and subtraction-based Ys to quantify the probabilistic difference. Three models series, nonlinear Logistic and Henon series and linear Gaussian series, and their surrogate data sets are employed to testify our proposed method. Since equal values are not rare in heartbeats, the effects of equal RR intervals on the probability distributions of order patterns and on the permutation-based nonlinearity detection are verified, and the probabilistic divergence of equality-involved permutations for heartbeats has more reliable outcomes that are in line with the complexity losing theory about diseased and aging heartbeats. The probabilistic divergence of permutations is not affected by forbidden permutation and is effective to quantify the nonlinear behaviors.

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