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.

scholarly journals Measuring the Topological Time Irreversibility of Time Series With the Degree-Vector-Based Visibility Graph Method

2021 ◽  
Vol 9 ◽  
Author(s):  
Ryutaro Mori ◽  
Ruiyun Liu ◽  
Yu Chen
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Time Reversal ◽  
Financial Time Series ◽  
Visibility Graph ◽  
Topological Properties ◽  
Network Nodes ◽  
Financial Time ◽  
Time Irreversibility ◽  
Synthetic Time Series

Time irreversibility of a time series, which can be defined as the variance of properties under the time-reversal transformation, is a cardinal property of non-equilibrium systems and is associated with predictability in the study of financial time series. Recent pieces of literature have proposed the visibility-graph-based approaches that specifically refer to topological properties of the network mapped from a time series, with which one can quantify different degrees of time irreversibility within the sets of statistically time-asymmetric series. However, all these studies have inadequacies in capturing the time irreversibility of some important classes of time series. Here, we extend the visibility-graph-based method by introducing a degree vector associated with network nodes to represent the characteristic patterns of the index motion. The newly proposed method is parameter-free and temporally local. The validation to canonical synthetic time series, in the aspect of time (ir)reversibility, illustrates that our method can differentiate a non-Markovian additive random walk from an unbiased Markovian walk, as well as a GARCH time series from an unbiased multiplicative random walk. We further apply the method to the real-world financial time series and find that the price motions occasionally equip much higher time irreversibility than the calibrated GARCH model does.

Generalized Cumulative Residual Entropy of Time Series Based on Permutation Patterns

2021 ◽  
pp. 2150055
Author(s):  
Qin Zhou ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Stock Markets ◽  
Multiple Scales ◽  
Permutation Entropy ◽  
Residual Entropy ◽  
Permutation Patterns ◽  
Cumulative Residual Entropy ◽  
The Us ◽  
Cumulative Residual ◽  
Different Characteristics

Cumulative residual entropy (CRE) has been suggested as a new measure to quantify uncertainty of nonlinear time series signals. Combined with permutation entropy and Rényi entropy, we introduce a generalized measure of CRE at multiple scales, namely generalized cumulative residual entropy (GCRE), and further propose a modification of GCRE procedure by the weighting scheme — weighted generalized cumulative residual entropy (WGCRE). The GCRE and WGCRE methods are performed on the synthetic series to study properties of parameters and verify the validity of measuring complexity of the series. After that, the GCRE and WGCRE methods are applied to the US, European and Chinese stock markets. Through data analysis and statistics comparison, the proposed methods can effectively distinguish stock markets with different characteristics.

Multiscale weighted Rényi entropy causality plane for financial time series

2019 ◽  
Vol 30 (05) ◽  
pp. 1950037 ◽  
Author(s):  
Jing Gao ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Financial Time Series ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Market Development ◽  
Permutation Entropy ◽  
Statistical Measure ◽  
Stock Market Development ◽  
Financial Time

The permutation entropy (PE) is a statistical measure which can describe complexity of time series. In recent years, the research on PE is increasing gradually. As part of its application, the complexity–entropy causality plane (CECP) and weighted CECP (WCECP) have been recently used to distinguish the stage of stock market development. In this paper, we focus on weighted Rényi entropy causality plane (WRECP), and then extend WCECP and WRECP into multiscale WCECP (MWCECP) and multiscale WRECP (MWRECP) by introducing a new parameter scale. By data simulating and analyzing, we show the power of WRECP. Besides, we discuss the MWCECP and the MWRECP of adjacent scales. It reveals a gradual relationship between adjacent weighted scale entropies.

scholarly journals Permutation Entropy and Irreversibility in Gait Kinematic Time Series from Patients with Mild Cognitive Decline and Early Alzheimer’s Dementia

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 868 ◽  
Author(s):  
Juan-Andrés Martín-Gonzalo ◽  
Irene Pulido-Valdeolivas ◽  
Yu Wang ◽  
Ting Wang ◽  
Guadalupe Chiclana-Actis ◽  
...  
Keyword(s):  
Time Series ◽  
Cognitive Impairment ◽  
Cognitive Decline ◽  
Permutation Entropy ◽  
Permutation Patterns ◽  
Compensatory Mechanisms ◽  
Neurodegenerative Dementias ◽  
Late Stages ◽  
Potential Use

Gait is a basic cognitive purposeful action that has been shown to be altered in late stages of neurodegenerative dementias. Nevertheless, alterations are less clear in mild forms of dementia, and the potential use of gait analysis as a biomarker of initial cognitive decline has hitherto mostly been neglected. Herein, we report the results of a study of gait kinematic time series for two groups of patients (mild cognitive impairment and mild Alzheimer’s disease) and a group of matched control subjects. Two metrics based on permutation patterns are considered, respectively measuring the complexity and irreversibility of the time series. Results indicate that kinematic disorganisation is present in early phases of cognitive impairment; in addition, they depict a rich scenario, in which some joint movements display an increased complexity and irreversibility, while others a marked decrease. Beyond their potential use as biomarkers, complexity and irreversibility metrics can open a new door to the understanding of the role of the nervous system in gait, as well as its adaptation and compensatory mechanisms.

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.

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