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The multiscale large deviation spectrum based on higher moments for financial time series

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Abstract

In this letter, based on large deviations theory, we propose to use higher moments (e.g., skewness, kurtosis) to investigate the multifractal features of large deviations spectrum. It is different from the estimation of the spectrum using another roughness exponent, such as oscillation-based grain exponent. When using statistical skewness and kurtosis as roughness exponent, the traditional normalization procedure of signals fails. To overcome this problem, a new approach is proposed. The large deviations spectrum on both artificial and financial time series is estimated. Comparing with another multifractal analysis, we verify that large deviations spectrum overcomes the limitations of Legendre spectrum, and the proposed method is able to reveal significant information that remains hidden with Legendre spectrum. The properties of scaling behavior using a modified scaling/non-scaling criterion are discussed. Meanwhile, we study the scaling behavior of time series and quantify the presence or absence of scale invariance of financial signals.

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Acknowledgements

The financial supports from the funds of the Fundamental Research Funds for the Central Universities (2018JBZ104), the China National Science (61771035), the Beijing National Science (4162047) and China Postdoctoral Science Foundation (043206005) are gratefully acknowledged.

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Authors and Affiliations

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

    Shijian Chen & Pengjian Shang

  2. State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing, China

    Wenbin Shi

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  1. Shijian Chen
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  2. Wenbin Shi
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Correspondence to Shijian Chen.

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Chen, S., Shi, W. & Shang, P. The multiscale large deviation spectrum based on higher moments for financial time series. Nonlinear Dyn 94, 597–613 (2018). https://doi.org/10.1007/s11071-018-4379-7

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