MEASURING STRUCTURAL CHANGES OF RECURRENCE PATTERNS IN MULTIFRACTAL AND MULTISCALE ASPECTS BY GENERALIZED RECURRENCE LACUNARITY

Xuegeng Mao, Zezhou Liu, Jinzhao Liu, Wanru Xie, Pengjian Shang and Zhiwei Shao
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Xuegeng Mao: Infrastructure Inspection Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing 100081, P. R. China
Zezhou Liu: ��Graduate Department, China Academy of Railway Sciences, Beijing 100081, P. R. China
Jinzhao Liu: Infrastructure Inspection Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing 100081, P. R. China
Wanru Xie: Infrastructure Inspection Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing 100081, P. R. China
Pengjian Shang: ��School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, P. R. China
Zhiwei Shao: Infrastructure Inspection Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing 100081, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 01, 1-19

Abstract: Recurrence lacunarity has been recently proposed to detect dynamical state transitions over various temporal scales. In this paper, we combine suggested distribution moments and introduce multifractal recurrence lacunarity to unearth rich information of trajectories in phase space. By considering generalized moments, it provides an enhanced measurement to account for differences of black pixels in the recurrence plot at various scales. Numerical simulations have proved that the proposed method is able to differentiate varying types of time series and provide further insights of inherent features including stochastic series, chaotic maps and series contaminated interference components. In real-world applications, it performs well on quantifying the subtle structural changes of financial time series. In addition, it is intriguing to confirm that corrugation signals possess much more vivid information of heterogeneity in terms of recurrence plots than normal ones.

Keywords: Multifractal Recurrence Lacunarity; Recurrence Plot; Dynamical State Transitions; Financial Time Series; Abnormity Diagnosis; Rail Corrugation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500178

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