| Most complex systems exist in the real world,studying the time series of complex systems is an effective method to analyze its own structure and dynamic evolution.Classical theoretical methods are mainly used to study stationary series.Since the time series of complex systems are mostly non-stationary,the cross-correlation and partial correlation of non-stationary time series are studied by using methods based on multifractal analysis and detrended theory here.Firstly,based on the multifractal detrended cross-correlation analysis and partial correlation analysis,the multifractal detrended partial cross-correlation analysis is proposed.The autoregressive fractionally integrated moving average process is used to verify the effectiveness of this method.Partial cross-correlation method and the influence of time delay on the correlation are studied under different scales.And two different actual time series,time series of the stock market and the aeroengine gas path parameters,are analyzed respectively.Secondly,the Moran index of the detrended time series is proposed to analyze the spatial correlation.Different spatial weight matrices are constructed by the application of multifractal detrended cross-correlation analysis and multifractal detrended partial cross-correlation analysis.The Moran index calculated based on different spatial weight matrices is used to determine the optimal spatial weight matrix required by the spatial econometric model.Finally,the spatial econometric model is established on the basis of the optimal spatial weight matrix,to predict the non-stationary time series.By comparing the results of the spatial Durbin model and the nearest neighbor algorithm,it is turns out that the prediction result obtained by the spatial Durbin model is closer to the actual value.Therefore,the application of the spatial Durbin model can predict the stock market better. |
