Multidimensional Time Series Analysis Based On An Improved Multidimensional Recursive Analysis Method

Recurrence is the fundamental characteristic of many complex dynamic systems,which has been studied and applied for a long time in the field of chaos.Recurrence plot and its recurrence quantification analysis technology is an important technology to study the recurrence characteristics of complex dynamic system.The basic recurrence plot and its recurrence quantification analysis technology is based on one-dimensional time series.However,this method is obviously not suitable for the study of multidimensional time series.Based on this fact,the multidimensional recurrence plot and its recurrence quantification analysis technology came into being,and at present,there is a few people use multidimensional recurrence analysis to investigate the multidimensional time series,thus multidimensional recurrence analysis of multidimensional time series is the focus of this paper.In this paper,we firstly study the autocorrelation of a group of multidimensional time series.In order to further exploring the dynamic information of multidimensional time series,we combine the wavelet packet decomposition and ensemble empirical mode decomposition with multidimensional recurrence analysis method respectively,and propose two multiscale multidimensional recurrence analysis methods,namely multiwavelet scale multidimensional recurrence quantification analysis based on wavelet packet decomposition(MWMRQA)and the multiscale multidimensional recurrence quantification analysis method with ensemble empirical mode decomposition(MdRQA-EEMD).These two methods can decompose the multidimensional time series into small scales of different time or frequency,which is conducive to the study of the dynamic information hidden in the time series.Secondly,this paper studies the cross correlation between two groups of multidimensional time series,and proposes multiscale cross recurrence analysis(MSCRQA)and multiscale multidimensional cross recurrence quantification(MMDCRQA)methods based on coarse-grained.Where MSCRQA method is suitable for studying the cross correlation between two one-dimensional time series.However,in the real world,some complex systems are multivariable,which limits the analysis of the internal multiple time series.Therefore,we extend one-dimensional MSCRQA method to multidimensional MMDCRQA method,thus we can not only study the correlation between two one-dimensional time series under different time scales,but also the correlation between the systems where the two one-dimensional time series are located.Finally,we use the concept of fuzzy membership to measure the similarity between the phase space states,and propose the fuzzy multidimensional recurrence plot(FMRP)and the fuzzy multidimensional cross recurrence plot(FMCRP).These two methods can visualize the recurrence of the phase space state as a gray-scale texture,and provide richer information for pattern analysis,and both use the number of cluster centers to replace the similarity threshold required by the traditional recurrence plot.The estimation of the parameters of the FMCRP method is smaller than that of the traditional recurrence plot method.These two kinds of recurrence state can be visualized as gray texture,which provides more information for pattern analysis.They use cluster center number instead of the similarity threshold required by traditional recurrence plot,so that FMRP and FMCRP methods can show advantages in parameter selection.