因果关系和熵-复杂度平面：鲁棒性和缺失有序模式
Causality and the Entropy-Complexity Plane: Robustness and Missing Ordinal Patterns
摘要：
我们在这里处理时间序列中的决定论与随机性的问题。人们希望确定它们在给定时间序列中的相对权重。在文献中已经提出了两种不同的工具来达到这种效果，即，i）“因果”熵-复杂性平面[Rosso等人，Phys. Rev. Lett. 99（2007）154102]和ii）缺失有序模式的衰减率的估计[Amigó等人，Europhys. Lett. 79（2007）50001和Carpi等人Physica A 389（2010）2020-2029]。在这项工作中，我们扩展使用这些技术，以解决污染的加性噪声的不同程度的相关性的确定性有限时间序列的分析。这里研究的混沌序列是通过Logistic映射（r = 4），我们添加了相关噪声（有色噪声与f-k功率谱，0 { \leq } k { \leq } 2）的变化幅度。以这种方式，可以获得与原始时间序列的确定性组成部分有关的重要见解。我们发现，在熵复杂度平面，这个目标可以实现，而无需额外的计算。
英文摘要：
We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, i) the "causal" entropy-complexity plane [Rosso et al. Phys. Rev. Lett. 99 (2007) 154102] and ii) the estimation of the decay rate of missing ordinal patterns [Amigó et al. Europhys. Lett. 79 (2007) 50001, and Carpi et al. Physica A 389 (2010) 2020-2029]. In this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation. The chaotic series studied here was via the logistic map (r = 4) to which we added correlated noise (colored noise with f-k Power Spectrum, 0 {\leq} k {\leq} 2) of varying amplitudes. In such a fashion important insights pertaining to the deterministic component of the original time series can be gained. We find that in the entropy-complexity plane this goal can be achieved without additional computations.
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