Missing ordinal patterns in correlated noises

Carpi, Laura C.; Saco, Patricia M.; Rosso, Osvaldo A.

doi:10.1016/j.physa.2010.01.030

Cited by 49 publications

(64 citation statements)

References 39 publications

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“…In other words, missing ordinal patterns are more persistent in the time series with higher correlation structures. Carpi et al [30] also have shown that the standard deviation of the estimated decay rate of missing ordinal patterns decreases with increasing D. This is due to the fact that longer patterns contain more temporal information and are therefore more effective in capturing the dynamics of time series with correlation structures.…”

Section: Distinguishing Noise From Chaosmentioning

confidence: 98%

“…Moreover, analytical expressions can be derived [29] for some stochastic processes (i.e., fractional Brownian motion for PDF's based on ordinal patterns with length 2 ≤ D ≤ 4). The methodology of Amigó was recently extended by Carpi et al [30] for the analysis of such stochastic processes: specifically, fractional Brownian motion (fBm), fractional Gaussian noise (fGn), and noises with f −k power spectrum and (k ≥ 0). More precisely, they analyzed the decay rate of missing ordinal patterns as a function of pattern-length D (embedding dimension) and of time series length N .…”

Section: Distinguishing Noise From Chaosmentioning

confidence: 99%

See 1 more Smart Citation

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Zanin

Zunino

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et al. 2012

Entropy

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Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, Entropy 2012, 14 1554 as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.

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Section: Distinguishing Noise From Chaosmentioning

confidence: 98%

Section: Distinguishing Noise From Chaosmentioning

confidence: 99%

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Zanin

Zunino

Rosso

et al. 2012

Entropy

542

432

View full text Add to dashboard Cite

show abstract

“…The NumFW, also known as missing patterns, outperformed SampEn in group differentiation. True missing patterns are robust against noise and they have the potential ability for distinguishing deterministic behavior from randomness in finite time series contaminated with observational white noise [41,42].…”

Section: Discussionmentioning

confidence: 99%

Symbolic Entropy of the Amplitude rather than the Instantaneous Frequency of EEG Varies in Dementia

Lin

Tsao

et al. 2015

Entropy

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Abstract:The dynamics of human electroencephalography (EEG) have been proved to be related to cognitive activities. This study separately assessed the two EEG components, amplitude and rhythm, aiming to capture their individual contributions to cognitive functions. We extracted the local peaks of EEGs under rest or photic stimulation and calculated the symbolic dynamics of their voltages (amplitude) and interpeak intervals (instantaneous frequency), individually. The sample consisted of 89 geriatric outpatients in three patient groups: 38 fresh cases of vascular dementia (VD), 22 fresh cases of Alzheimer's disease (AD) and 29 controls. Both sample entropy and number of forbidden words revealed significantly less regular symbolic dynamics in the whole EEG tracings of the VD than the AD and control groups. We found consistent results between groups with the symbolic dynamics in the local-peak voltage sequence rather than the interpeak interval sequence. Photic stimulation amplified the differences between groups. These results suggest that the EEG dynamics which relates to either cognitive functions or the underlying pathologies of dementia are embedded within the dynamics of the amount of but not the interval between each synchronized firing of adjacent cerebral neurons.

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“…Symbolic time series analysis is a powerful technique able to extract hidden features such as the presence of frequent recurrent patterns [1][2][3][4][5], or the existence of missing/forbidden patterns [6][7][8] from stochastic, highdimensional signals. Symbolic analysis has also proven to be useful for classifying different types of signals [9][10][11][12] and, in bivariate analysis, for inferring the direction of information flow [13,14].…”

Section: Introductionmentioning

confidence: 99%

Quantifying sudden changes in dynamical systems using symbolic networks

et al. 2015

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We characterize the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time series we construct a network in which every node weight represents the probability of an ordinal pattern (OP) to appear in the symbolic sequence and each edgeʼs weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent, and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions.

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Missing ordinal patterns in correlated noises

Cited by 49 publications

References 39 publications

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Symbolic Entropy of the Amplitude rather than the Instantaneous Frequency of EEG Varies in Dementia

Quantifying sudden changes in dynamical systems using symbolic networks

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