Relative asynchronous index: a new measure for time series irreversibility

In this paper, we suggest a new measure for testing reversibility of time series which combines two different tools: the visibility algorithm and the inversion number. First, the visibility algorithm maps the time series to the network according to a geometric criterion. After that, the degree of ir...

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Published in:	Nonlinear dynamics Vol. 93; no. 3; pp. 1545 - 1557
Main Authors:	Yang, Pengbo, Shang, Pengjian
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.08.2018 Springer Nature B.V
Subjects:	Algorithms Automotive Engineering Classical Mechanics Control Dynamical Systems Engineering Mechanical Engineering Multiscale analysis Original Paper Parameter estimation Regression analysis Sequences Time series Vibration Visibility Degree sequences Financial time series Visibility algorithm Inversion number Relative asynchronous index
ISSN:	0924-090X, 1573-269X
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Abstract	In this paper, we suggest a new measure for testing reversibility of time series which combines two different tools: the visibility algorithm and the inversion number. First, the visibility algorithm maps the time series to the network according to a geometric criterion. After that, the degree of irreversibility of the time series can be estimated by the relative asynchronous index (RAI), based on the inverse number, between out and out ∗ degree sequences of the network (out and out ∗ represent the outgoing sequence of forward time series and reverse time series, respectively). This method does not need to rely on additional parameters, so it can avoid the error caused by parameter estimation. In addition, we also study the multiscale RAI and find that the optimal scale selection for detection time irreversibility is 1–4. Different types of time series are used to confirm the validity of this metric. Finally, we apply the method to financial time series and find that the financial crisis can be detected by RAI.
AbstractList	In this paper, we suggest a new measure for testing reversibility of time series which combines two different tools: the visibility algorithm and the inversion number. First, the visibility algorithm maps the time series to the network according to a geometric criterion. After that, the degree of irreversibility of the time series can be estimated by the relative asynchronous index (RAI), based on the inverse number, between out and out ∗ degree sequences of the network (out and out ∗ represent the outgoing sequence of forward time series and reverse time series, respectively). This method does not need to rely on additional parameters, so it can avoid the error caused by parameter estimation. In addition, we also study the multiscale RAI and find that the optimal scale selection for detection time irreversibility is 1–4. Different types of time series are used to confirm the validity of this metric. Finally, we apply the method to financial time series and find that the financial crisis can be detected by RAI. In this paper, we suggest a new measure for testing reversibility of time series which combines two different tools: the visibility algorithm and the inversion number. First, the visibility algorithm maps the time series to the network according to a geometric criterion. After that, the degree of irreversibility of the time series can be estimated by the relative asynchronous index (RAI), based on the inverse number, between out and \[\hbox {out}^\] degree sequences of the network (out and \[\hbox {out}^\] represent the outgoing sequence of forward time series and reverse time series, respectively). This method does not need to rely on additional parameters, so it can avoid the error caused by parameter estimation. In addition, we also study the multiscale RAI and find that the optimal scale selection for detection time irreversibility is 1–4. Different types of time series are used to confirm the validity of this metric. Finally, we apply the method to financial time series and find that the financial crisis can be detected by RAI. In this paper, we suggest a new measure for testing reversibility of time series which combines two different tools: the visibility algorithm and the inversion number. First, the visibility algorithm maps the time series to the network according to a geometric criterion. After that, the degree of irreversibility of the time series can be estimated by the relative asynchronous index (RAI), based on the inverse number, between out and out∗ degree sequences of the network (out and out∗ represent the outgoing sequence of forward time series and reverse time series, respectively). This method does not need to rely on additional parameters, so it can avoid the error caused by parameter estimation. In addition, we also study the multiscale RAI and find that the optimal scale selection for detection time irreversibility is 1–4. Different types of time series are used to confirm the validity of this metric. Finally, we apply the method to financial time series and find that the financial crisis can be detected by RAI.
Author	Shang, Pengjian Yang, Pengbo
Author_xml	– sequence: 1 givenname: Pengbo surname: Yang fullname: Yang, Pengbo organization: Department of Mathematics, School of Science, Beijing Jiaotong University – sequence: 2 givenname: Pengjian surname: Shang fullname: Shang, Pengjian email: pjshang@bjtu.edu.cn organization: Department of Mathematics, School of Science, Beijing Jiaotong University
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Snippet	In this paper, we suggest a new measure for testing reversibility of time series which combines two different tools: the visibility algorithm and the inversion...
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SubjectTerms	Algorithms Automotive Engineering Classical Mechanics Control Dynamical Systems Engineering Mechanical Engineering Multiscale analysis Original Paper Parameter estimation Regression analysis Sequences Time series Vibration Visibility
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Title	Relative asynchronous index: a new measure for time series irreversibility
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