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Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 513–528 | Cite as

Multifractal and recurrence behaviors of continuum percolation-based financial price dynamics

  • Hongli Niu
  • Jun Wang
Original Paper

Abstract

The modeling of financial price fluctuations is always a hot research aspect that many researchers are concerned about. A financial price model based on two-dimensional continuum percolation system, which is one of the most important statistical physics systems, is introduced in this work. In the model, the fluctuations of stock price changes are assumed to be attributed to the market information interactions among the traders, and the percolation cluster is taken to represent the traders holding the same investment attitude. Then, multifractal detrended fluctuation analysis method is adopted to study the multifractal behaviors of simulation data with different parameter sets. Finally, the recurrence plot and recurrence quantification analysis techniques are applied to investigate the complex determinism dynamics hidden in the simulated stock returns from the price model, as well as in their different intrinsic mode functions (IMFs) decomposed from the empirical mode decomposition method. Abundant and distinctive recurrence behaviors can be observed among returns and IMFs time series. In the meanwhile, the corresponding behaviors of the Chinese Shanghai Composite Index is studied for comparison.

Keywords

Financial time series Continuum percolation system  MF-DFA Recurrence plot Recurrence quantification analysis 

Abbreviations

MF-DFA

Multifractal detrended fluctuation analysis

EMD

Empirical mode decomposition

IMF

Intrinsic mode function

IMF1

The first intrinsic mode function

IMF2

The second intrinsic mode function

RP

Recurrence plot

RQA

Recurrence quantification analysis

RR

Recurrence rate

DET

Determinism

\(L_{{\text{ ENT }}}\)

Shannon entropy

LAM

Laminarity

TT

Trapping time

Notes

Acknowledgments

The authors were supported by the Fundamental Research Funds for the Central Universities No. 2015YJS180, by National Natural Science Foundation of China Grant No. 71271026 and Grant No. 10971010.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institute of Financial Mathematics and Financial Engineering, School of ScienceBeijing Jiaotong UniversityBeijingP. R. China

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