Multiwavelet scale multidimensional recurrence quantification analysis.

The multiwavelet scale multidimensional recurrence quantification analysis (MWMRQA) method is proposed in this paper, which is a combination of multidimensional recurrence quantification analysis and wavelet packet decomposition. It allows us to quantify the recurrence properties of a single multidimensional time series under different wavelet scales. We apply the MWMRQA method to the Lorenz system and the Chinese stock market, respectively, and show the feasibility of this method as well as the dynamic variation of the Lorenz system and the Chinese stock market under different wavelet scales. This provides another perspective for other disciplines that need to study the recurrence properties of different scales in the future.

[1]  Seong‐Min Yoon,et al.  Dynamic co-movement between oil and stock markets in oil-importing and oil-exporting countries: Two types of wavelet analysis , 2020 .

[2]  Sebastian Wallot,et al.  Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab , 2018, Front. Psychol..

[3]  P. Crowley.  Analyzing convergence and synchronicity of business and growth cycles in the euro area using cross recurrence plots , 2008 .

[4]  Jingjing Huang,et al.  Multifractal detrended fluctuation analysis on high-frequency SZSE in Chinese stock market , 2019, Physica A: Statistical Mechanics and its Applications.

[5]  V. Plerou,et al.  Scaling of the distribution of fluctuations of financial market indices. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Pengjian Shang,et al.  Multidimensional k-nearest neighbor model based on EEMD for financial time series forecasting , 2017 .

[7]  Pengjian Shang,et al.  Multifractal cross-correlation spectra analysis on Chinese stock markets , 2014 .

[8]  Hui Yang,et al.  Multiscale recurrence analysis of long-term nonlinear and nonstationary time series , 2012 .

[9]  Zhigang Zeng,et al.  Pigeon-inspired optimization and extreme learning machine via wavelet packet analysis for predicting bulk commodity futures prices , 2019, Science China Information Sciences.

[10]  A. Giuliani,et al.  Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification , 1998 .

[11]  Pengjian Shang,et al.  Multifractal diffusion entropy analysis on stock volatility in financial markets , 2012 .

[12]  Plamen Ch. Ivanov,et al.  Dynamic network interactions among distinct brain rhythms as a hallmark of physiologic state and function , 2020, Communications Biology.

[13]  Fourier Filtering for Minimizing the Periodic Trend Effects on Multifractal Diffusion Entropy Analysis , 2014 .

[14]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[15]  Norbert Marwan,et al.  A historical review of recurrence plots , 2008, 1709.09971.

[16]  Plamen Ch Ivanov,et al.  Delay-correlation landscape reveals characteristic time delays of brain rhythms and heart interactions , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[17]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[18]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[19]  J. Zbilut,et al.  Embeddings and delays as derived from quantification of recurrence plots , 1992 .

[20]  Sebastian Wallot,et al.  Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) – A Method for Quantifying Correlation between Multivariate Time-Series , 2018, Multivariate behavioral research.

[21]  Pengjian Shang,et al.  Multiscale multifractal diffusion entropy analysis of financial time series , 2015 .

[22]  Sebastian Wallot,et al.  Multidimensional Recurrence Quantification Analysis (MdRQA) for the Analysis of Multidimensional Time-Series: A Software Implementation in MATLAB and Its Application to Group-Level Data in Joint Action , 2016, Front. Psychol..

[24]  Jingjing Huang.  Multiscale Diffusion Entropy Analysis on Traffic Index Series , 2014 .

[25]  Xiaoming Liu,et al.  Fractional frequency hybrid model based on EEMD for financial time series forecasting , 2020, Commun. Nonlinear Sci. Numer. Simul..