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Relative asynchronous index: a new measure for time series irreversibility

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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 \(\hbox {out}^*\) 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.

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Acknowledgements

The financial supports from the Funds of the China National Science (61771035) and the Beijing National Science (4162047) are gratefully acknowledged.

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  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Pengbo Yang & Pengjian Shang

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  1. Pengbo Yang
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Correspondence to Pengjian Shang.

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Yang, P., Shang, P. Relative asynchronous index: a new measure for time series irreversibility. Nonlinear Dyn 93, 1545–1557 (2018). https://doi.org/10.1007/s11071-018-4275-1

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