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Estimation on complexity of time series using generalized distance components statistics

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Abstract

In this paper, we propose the generalized distance components (GDISCO) approach that enables us to estimate the complexity of time series from the perspectives of time and space. This approach is based on the rotational invariance of energy distance in high-dimensional space. Compared with the existing complexity measures, the main innovation of the GDISCO method is that it not only gives the total complexity, but also calculates the complexity within and between the components of pooled samples. We verify the effectiveness of this method for studying and dividing the spatial complexity of periodic, chaotic and stochastic processes and some common probability distribution through simulated data. The results illustrate that the variation of GDISCO is monotonic and consistent as the change of parameters. The multivariate data are also experimented, it mainly confirms that the between-sample dispersion statistic of GDISCO can evaluate the similarity among the structure of the components of pooled samples. Then, we apply this approach to study physiological RR internal time series to detect the efficacy of drugs for the treatment of suppress arrhythmias in survivors of myocardial infarction. Besides, it is used to analyze the properties and differences of Chinese and American stock markets. It all shows excellent performance.

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Data Availability Statement

The financial dataset generated during and analyzed during the current study are available in the finance of yahoo, [http://finance.yahoo.com/]. The CAST RR interval dataset is publicly available in the Physionet, [https://physionet.org/].

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Acknowledgements

The financial supports from the funds of the Fundamental Research Funds for the Central Universities (2021YJS166) are gratefully acknowledged.

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  1. Department of Mathematics, School of Science, Jiaotong University, Beijing, 100044, China

    Zhuo Wang & Pengjian Shang

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  1. Zhuo Wang
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  2. Pengjian Shang
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Correspondence to Zhuo Wang.

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Wang, Z., Shang, P. Estimation on complexity of time series using generalized distance components statistics. Nonlinear Dyn 107, 3709–3727 (2022). https://doi.org/10.1007/s11071-021-07168-7

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