Using forbidden ordinal patterns to detect determinism in irregularly sampled time series

2016 ◽  
Vol 26 (2) ◽  
pp. 023107 ◽  
Author(s):  
C. W. Kulp ◽  
J. M. Chobot ◽  
B. J. Niskala ◽  
C. J. Needhammer
Keyword(s):  
Time Series ◽  
Ordinal Patterns

scholarly journals Detection of time reversibility in time series by ordinal patterns analysis

2018 ◽  
Vol 28 (12) ◽  
pp. 123111 ◽  
Author(s):  
J. H. Martínez ◽  
J. L. Herrera-Diestra ◽  
M. Chavez
Keyword(s):  
Time Series ◽  
Time Reversibility ◽  
Ordinal Patterns

Symbolic Analysis of High-Dimensional Time Series

2003 ◽  
Vol 13 (09) ◽  
pp. 2657-2668 ◽  
Author(s):  
Karsten Keller ◽  
Heinz Lauffer
Keyword(s):  
Time Series ◽  
Symbolic Dynamics ◽  
Epileptic Activity ◽  
High Dimensional ◽  
Qualitative Information ◽  
Eeg Data ◽  
Ordinal Patterns ◽  
The Given ◽  
Matrix Series ◽  
Qualitative Changes

In order to extract and to visualize qualitative information from a high-dimensional time series, we apply ideas from symbolic dynamics. Counting certain ordinal patterns in the given series, we obtain a series of matrices whose entries are symbol frequencies. This matrix series is explored by simple methods from nominal statistics and information theory. The method is applied to detect and visualize qualitative changes of EEG data related to epileptic activity.

scholarly journals Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1013 ◽  
Author(s):  
David Cuesta-Frau ◽  
Antonio Molina-Picó ◽  
Borja Vargas ◽  
Paula González
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Classification Accuracy ◽  
Markov Models ◽  
Hidden Markov ◽  
Permutation Entropy ◽  
Time Series Classification ◽  
Discriminating Power ◽  
Ordinal Patterns ◽  
Temperature Records

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear I R n mapping into I R , where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.

scholarly journals Ordinal Patterns in Heartbeat Time Series: An Approach Using Multiscale Analysis

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 583 ◽  
Author(s):  
María Muñoz-Guillermo
Keyword(s):  
Time Series ◽  
Multiscale Analysis ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Cardiac Diseases ◽  
Ordinal Patterns

In this paper, we simultaneously use two different scales in the analysis of ordinal patterns to measure the complexity of the dynamics of heartbeat time series. Rényi entropy and weighted Rényi entropy are the entropy-like measures proposed in the multiscale analysis in which, with the new scheme, four parameters are involved. First, the influence of the variation of the new parameters in the entropy values is analyzed when different groups of subjects (with cardiac diseases or healthy) are considered. Secondly, we exploit the introduction of multiscale analysis in order to detect differences between the groups.

Revisiting the decay of missing ordinal patterns in long-term correlated time series

2019 ◽  
Vol 534 ◽  
pp. 122100 ◽  
Author(s):  
Felipe Olivares ◽  
Luciano Zunino ◽  
Dario G. Pérez
Keyword(s):  
Time Series ◽  
Ordinal Patterns

THE ORDINAL STRUCTURE OF THE SIGNED SHIFT TRANSFORMATIONS

2009 ◽  
Vol 19 (10) ◽  
pp. 3311-3327 ◽  
Author(s):  
JOSÉ MARÍA AMIGÓ
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Entropy Estimation ◽  
Series Analysis ◽  
Ordinal Patterns ◽  
The One ◽  
Baker Map

Ordinal patterns bring in the dynamic novel aspects, difficult questions, and useful tools for entropy estimation, time series analysis and other applications. In [Amigó et al., 2008a], the structure of the ordinal patterns of the one- and two-sided shifts on N symbols was elucidated with great detail. The results are applied via order isomorphy to the ordinal structure of the sawtooth maps x ↦ Nx mod 1 and the baker map. In this paper, we generalize the technique employed there, to cope with the so-called signed shifts on N symbols and signed sawtooth maps.

scholarly journals Forecasting Events in the Chaotic Dynamics of a Fiber Laser

2018 ◽  
Author(s):  
Andrés Aragoneses ◽  
Yingqi Ding
Keyword(s):  
Time Series ◽  
Fiber Laser ◽  
Chaotic Dynamics ◽  
High Threshold ◽  
Output Intensity ◽  
Low Intensity ◽  
Temporal Correlations ◽  
Low Threshold ◽  
Ordinal Patterns ◽  
Brain Behavior

Being able to forecast events is of great importance in many fields, from brain behavior to earthquakes or stock markets. Because each dynamical system has intrinsic features, different statistical tools have to be used for each system. Here we study the time series of the output intensity of a fiber laser with an ordinal patterns analysis, and we look for temporal correlations in order to statistically forecast the most intense events. We set two thresholds, a low one and a high one, to distinguish between low intensity versus high intensity events. We find that when the time series is performing events below the low threshold it shows some preferred temporal patterns before performing events above a high threshold.

Non-parametric analysis of serial dependence in time series using ordinal patterns

2021 ◽  
pp. 107381
Author(s):  
Christian H. Weiß ◽  
Manuel Ruiz Marín ◽  
Karsten Keller ◽  
Mariano Matilla-García
Keyword(s):  
Time Series ◽  
Parametric Analysis ◽  
Serial Dependence ◽  
Ordinal Patterns ◽  
Non Parametric

scholarly journals Teaching Ordinal Patterns to a Computer: Efficient Encoding Algorithms Based on the Lehmer Code

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1023 ◽  
Author(s):  
Sebastian Berger ◽  
Andrii Kravtsiv ◽  
Gerhard Schneider ◽  
Denis Jordan
Keyword(s):  
Time Series ◽  
Computational Cost ◽  
Permutation Entropy ◽  
Sequence Length ◽  
Compact Representation ◽  
Common Basis ◽  
Symbolic Transfer Entropy ◽  
Ordinal Patterns ◽  
Language Bindings ◽  
Lehmer Code

Ordinal patterns are the common basis of various techniques used in the study of dynamical systems and nonlinear time series analysis. The present article focusses on the computational problem of turning time series into sequences of ordinal patterns. In a first step, a numerical encoding scheme for ordinal patterns is proposed. Utilising the classical Lehmer code, it enumerates ordinal patterns by consecutive non-negative integers, starting from zero. This compact representation considerably simplifies working with ordinal patterns in the digital domain. Subsequently, three algorithms for the efficient extraction of ordinal patterns from time series are discussed, including previously published approaches that can be adapted to the Lehmer code. The respective strengths and weaknesses of those algorithms are discussed, and further substantiated by benchmark results. One of the algorithms stands out in terms of scalability: its run-time increases linearly with both the pattern order and the sequence length, while its memory footprint is practically negligible. These properties enable the study of high-dimensional pattern spaces at low computational cost. In summary, the tools described herein may improve the efficiency of virtually any ordinal pattern-based analysis method, among them quantitative measures like permutation entropy and symbolic transfer entropy, but also techniques like forbidden pattern identification. Moreover, the concepts presented may allow for putting ideas into practice that up to now had been hindered by computational burden. To enable smooth evaluation, a function library written in the C programming language, as well as language bindings and native implementations for various numerical computation environments are provided in the supplements.

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