scholarly journals Estimating entropy rate from censored symbolic time series: A test for time-irreversibility

2021 ◽  
Vol 31 (1) ◽  
pp. 013131
Author(s):  
R. Salgado-García ◽  
Cesar Maldonado
Keyword(s):  
Time Series ◽  
Entropy Rate ◽  
Time Irreversibility

scholarly journals Detecting Determinism in Time Series with Complex Networks Constructed Using a Compression Algorithm

2018 ◽  
Vol 28 (13) ◽  
pp. 1850165
Author(s):  
Débora C. Corrêa ◽  
David M. Walker ◽  
Michael Small
Keyword(s):  
Time Series ◽  
Complex Networks ◽  
Information Content ◽  
Compression Algorithm ◽  
Connectivity Structure ◽  
Cycle Basis ◽  
Minimal Cycle ◽  
Time Irreversibility ◽  
Basis Structure

The properties of complex networks derived from applying a compression algorithm to time series subject to symbolic ordinal-based encoding is explored. The information content of compression codewords can be used to detect forbidden symbolic patterns indicative of nonlinear determinism. The connectivity structure of ordinal-based compression networks summarized by their minimal cycle basis structure can also be used in tests for nonlinear determinism, in particular, detection of time irreversibility in a signal.

Information-Theoretic Characterization of Bifurcations in Nonlinear Dynamical Systems With Noise

2013 ◽  
Author(s):  
Navendu S. Patil ◽  
Joseph P. Cusumano
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Period Doubling ◽  
Entropy Rate ◽  
Series Data ◽  
High Dimensional ◽  
Dimensional System ◽  
Dimensional Manifold ◽  
Low Dimensional

Detecting bifurcations in noisy and/or high-dimensional physical systems is an important problem in nonlinear dynamics. Near bifurcations, the dynamics of even a high dimensional system is typically dominated by its behavior on a low dimensional manifold. Since the system is sensitive to perturbations near bifurcations, they can be detected by looking at the apparent deterministic structure generated by the interaction between the noise and low-dimensional dynamics. We use minimal hidden Markov models built from the noisy time series to quantify this deterministic structure at the period-doubling bifurcations in the two-well forced Duffing oscillator perturbed by noise. The apparent randomness in the system is characterized using the entropy rate of the discrete stochastic process generated by partitioning time series data. We show that as the bifurcation parameter is varied, sharp changes in the statistical complexity and the entropy rate can be used to locate incipient bifurcations.

scholarly journals The lack of reversibility during financial crisis and its identification

2021 ◽  
Vol 107 ◽  
pp. 03002
Author(s):  
Andrii Bielinskyi ◽  
Serhii Hushko ◽  
Andriy Matviychuk ◽  
Oleksandr Serdyuk ◽  
Serhiy Semerikov ◽  
...  
Keyword(s):  
Time Series ◽  
Stock Markets ◽  
Permutation Patterns ◽  
Financial Systems ◽  
Fundamental Idea ◽  
Nonlinear Properties ◽  
Time Irreversibility ◽  
Non Gaussian ◽  
Multiscale Time Irreversibility ◽  
Over Time

The focus of this study to measure the varying irreversibility of stock markets. A fundamental idea of this study is that financial systems are complex and nonlinear systems that are presented to be non-Gaussian fractal and chaotic. Their complexity and different aspects of nonlinear properties, such as time irreversibility, vary over time and for a long-range of scales. Therefore, our work presents approaches to measure the complexity and irreversibility of the time series. To the presented methods we include Guzik’s index, Porta’s index, Costa’s index, based on complex networks measures, Multiscale time irreversibility index and based on permutation patterns measures. Our study presents that the corresponding measures can be used as indicators or indicator-precursors of crisis states in stock markets.

scholarly journals Assessing Time Series Reversibility through Permutation Patterns

2018 ◽  
Author(s):  
Massimiliano Zanin ◽  
Alejandro Rodríguez González ◽  
Ernestina Menasalvas Ruiz ◽  
David Papo
Keyword(s):  
Time Series ◽  
Time Reversal ◽  
Financial Time Series ◽  
Statistical Tests ◽  
Fundamental Property ◽  
Permutation Entropy ◽  
Permutation Patterns ◽  
Visibility Graphs ◽  
Time Irreversibility ◽  
Financial Data Analysis

Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

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