Cross Correlation Analysis Of Time Series Based On Singular Spectrum Analysis

In order to better understand and describe complex systems,we often use time series as the basis for studying the internal laws of the system.At present,time series analysis has been applied in many fields and has achieved great development.However,most of the time series in the real world are non-stationary time series.Therefore,the study of nonlinear non-stationary time series has become a hot topic.The Detrended Cross-Correlation Analysis(DCCA)is used as a scaling exponent to investigate the long-range cross correlation of non-stationary time series.When cross correlation analysis is carried out on time series of trend signals,there will be cross point phenomenon and influence correlation analysis.Aiming at this phenomenon,a new adaptive time-frequency analysis method,Empirical Mode Decomposition(EMD)which has been developed in recent years,and applied to the study of nonlinear non-stationary time signals.Singular Spectrum Analysis(SSA),as a time series analysis technology,is suitable for analyzing data in nonlinear,non-stationary and noisy time series.It is mainly used to solve the problems of detection and extraction of trend or quasi periodic components,noise reduction,prediction,detection of abnormal points and so on.At present,the technology of singular spectrum analysis has been widely used in many fields,such as environment,medicine,finance and social science,and the effect of the analysis is very remarkable.Aiming at the common linear and exponential trend in time series,this paper proposes a new algorithm to remove the trend through singular trend analysis,and then use cross correlation analysis algorithm to eliminate intersection points in scale index diagram,which makes the analysis result more accurate.The Autoregressive Fractionally Integrated Moving Average models(ARFIMA)is used to produce two interrelated time sequences and overlay the trend,and the simulation experiments are carried out by using the Singular Spectrum Analysis.Through the analysis of the simulated data,comparing the Singular Spectrum Analysis with the Detrended Cross-Correlation Analysis and the Empirical Mode Decomposition.The results show that the Singular Spectrum Analysis solves the illusive correlation phenomenon of the Detrended Fluctuation Analysis and the Detrended Cross-Correlation Analysis in the process of signal processing,compared with the results of Detrended Fluctuation Analysis and Detrended Cross-Correlation Analysis directly dealing with linear and exponential trends.In addition,the simulation test shows that both the Singular Spectrum Analysis and the Empirical Mode Decomposition are both effectivedetrending schemes.However,compared with the empirical mode decomposition,the Detrended Fluctuation Analysis scale index and the Detrended Cross-Correlation Analysis scale index of the remaining time series after removing the trend in the Singular Spectrum Analysis are ideal.