Counting forbidden patterns in irregularly sampled time series. I. The effects of under-sampling, random depletion, and timing jitter

Abstract

It has been established that the count of ordinal patterns, which do not occur in a time series, called forbidden patterns, is an effective measure for the detection of determinism in noisy data. A very recent study has shown that this measure is also partially robust against the effects of irregular sampling. In this paper, we extend said research with an emphasis on exploring the parameter space for the method's sole parameter-the length of the ordinal patterns-and find that the measure is more robust to under-sampling and irregular sampling than previously reported. Using numerically generated data from the Lorenz system and the hyper-chaotic Rössler system, we investigate the reliability of the relative proportion of ordinal patterns in periodic and chaotic time series for various degrees of under-sampling, random depletion of data, and timing jitter. Discussion and interpretation of results focus on determining the limitations of the measure with respect to optimal parameter selection, the quantity of data available, the sampling period, and the Lyapunov and de-correlation times of the system.

Characterizing stochastic time series with ordinal networks

“…By knowing the exact form of random ordinal networks, we can also estimate the fraction of missing transi- tions in empirical time series. This analysis is somewhat similar to the one of missing permutations or forbidden patterns introduced by Amigó et al [30][31][32] and explored by several works [33][34][35]. These works have observed that some ordinal patterns cannot occur in chaotic systems [for instance, the permutation (2, 1, 0) never appears in logistic map under fully developed chaos] and that even stochastic processes may present missing ordinal patterns depending on the time series length and the choice of embedding dimension.…”

Macrophages use a bet-hedging strategy for antimicrobial activity in phagolysosomal acidification

“…To determine whether phagolysosomal acidification is a deterministic or stochastic dynamical process, we employed a permutation spectrum test (21) in which the distribution of ordinal patterns occurring in subsets of our full data set was analyzed ( Figure 1C). Ordinal patterns simply refer to the order of each measurement in terms of value, in our case the phagolysosomal pH, within a scanning window, which parses all measurements within each condition, exemplified in Figure 1 (22)(23)(24)(25). Here we found a 4-unit window size to be the most appropriate.…”

Twenty years after “The Impact of Chaos”: what have been achieved and what should be answered

“…I would like to pay attention how the researches of Refs. [74,[90][91][92] will develop in the future.…”