Multiscale Analysis And Application Of Multivariate Time Series Based On Adaptive Method

Fractal theory is one of the important branches of nonlinear science,which provides an effective method for understanding and characterizing the interactions of complex systems.In this thesis,based on the method of adaptive fractal analysis,we firstly study the fractal properties of cross-correlation of multivariate time series and establish the method of multivariate adaptive multifractal cross-correlation analysis(MV-AMFCCA).On the basis of what we mentioned above,to make the results more comprehensively depict the process of fractal properties varying with time scale,we add the multiscale analysis and propose the method of multiscale multivariate adaptive multifractal cross-correlation analysis(MMV-AMFCCA).By applying this method,we obtain the generalized three-dimensional Hurst exponent graph,which can characterize the fractal properties of cross-correlation in different time scales.Through experiments in simulated sequences,the results show that the method of MV-AMFCCA and MMV-AMFCCA are effective.Secondly,considering that the joint external factors will affect the cross-correlation analysis of multivariate time series,on the basis of MMV-AMFCCA,we introduce the partial cross-correlation analysis and establish the multiscale multivariate adaptive multifractal partial cross-correlation analysis(MMV-AMFPCCA).This method can characterize the fractal properties of the cross-correlation between the two multivariate systems after removing the influence of the third-party common factors on the two multivariate systems.In the experiments of numerical simulation sequences,the results show that the method can remove the influence of joint noise on the multivariate sequences and identify the monofractal and multifractal properties of the cross-correlation between multivariate sequences.Finally,we apply the proposed methods to the empirical study of stock market data in Asia and Europe,analyze the statistical characteristics and the fractal properties of the cross-correlation of the stock markets in the two regions.The results indicate that the properties of multifractality between the stock markets in the two regions are not only affected by joint external factors but also have time variability.