Permutation information theory approach to unveil delay dynamics from time series analysis
Zunino, Luciano; Soriano, Miguel C.; Fischer, I.; Rosso, Osvaldo A.; Mirasso, Claudio R.
Physical Review E 82, 046212 (1-9) (2010)
In this paper a novel approach to identify delay phenomena from time series is developed. We show that it is possible to perform a reliable time delay identiﬁcation by using quantiﬁers derived from information theory, more precisely, permutation entropy and permutation statistical complexity. These quantiﬁers show clear extrema when the embedding delay of the symbolic reconstruction matches the characteristic time delay of the system. Numerical data originating from a time delay system based on the well-known Mackey-Glass equations operating in the chaotic regime were used as test beds. We show that our method is straightforward to apply and robust to additive observational and dynamical noise. Moreover, we ﬁnd that the identiﬁcation of the time delay is even more eﬃcient in a noise environment. Our permutation approach is also able to recover the time delay in systems with low feedback rate or high nonlinearity.