Robust Detrended Cross-Correlation Analysis Of Nonstationary Time Series And Its Application

In the correlation study,Pearson correlation coefficient is a classical metrics.But in the study of cross correlation in non-stationary time series,due to ignore the trend of the sequence,nonstationarity and local dependency,Pearson correlation coefficient can't get effective measurements.Detrended cross-correlation analysis(DCCA)was proposed based on covariance can well solve these problems.Then in the process of its development,some studies have pointed out that outliers will have a significant impact on the method.However,outliers are common in the actual data,which will lead to inaccurate analysis results of cross-correlation between time series.Therefore,we consider the development of robust detrended cross-correlation analysis method to resist the adverse effects of outliers.As the key step of detrended cross-correlation analysis,the least square method is mostly used to fit the local trend,but the least square method is sensitive to outliers and is easily affected by outliers.Therefore,this paper uses the least absolute deviation(LAD)estimation method without iteration to replace the least square method to fit the local trend.However,only using robust method to fit the local trend is not enough,outliers will still affect the covariance and variance of time series,and then can not accurately detect the cross-correlation between time series.In this paper,combined with the least absolute deviation estimation,the nonparametric smooth local polynomial method is adopted,and the kernel function is introduced to calculate the variance and covariance of time series by weighting,we propose robust time weighted detrended cross-correlation analysis and robust local time weighted detrended cross-correlation analysis to obtain robust global and local cross-correlation analysis results when time series contain outliers.The simulation results conform that the robust time weighted detrended crosscorrelation analysis and its local method can accurately estimate the cross-correlation level between two non-stationary time series.Compared with the traditional detrended cross-correlation analysis and local detrended cross-correlation analysis,the experimental results show that when the proportion of outliers in two time series is 3%,6%,9%and 12%,the result of robust time weighted detrended cross-correlation analysis is more robust than traditional methods in resisting outliers.When the proportion of outliers is 3%,6%and 10%,compared with local detrended crosscorrelation analysis,robust local time weighted detrended cross-correlation analysis is less affected by outliers,and the higher the cross-correlation of time series itself,the more obvious the comparison between the robust method and the traditional method is in the robustness effect.Applying robust detrended cross-correlation analysis and its local methods to the cross-correlation study of stock market,and study the cross-correlation between stock markets in three regions,Chinese mainland,Hongkong and Taiwan,and the interrelationship between the three regions and the US and Japanese stock markets.This paper collects the historical daily closing prices of the CSI 300 index,Hang Seng Index,Taiwan weighted index,S&P 500 index and Nikkei 225 index from January 4,2016 to December 31,2020.The results show that the cross-correlation between Hong Kong and Taiwan is the highest,while that between Mainland and Hong Kong is the lowest.From a local perspective,the local cross-correlation between Hong Kong and Taiwan has always maintained a high level,while the cross-correlation between the mainland and Taiwan and Hong Kong has gradually strengthened.Generally speaking,there is a certain correlation between the three regions of China and the United States and Japan.From a local point of view,more information can be obtained.The correlation between the three regions of China and the stock markets of the United States and Japan has a trend of increasing over time,and the correlation with the stock markets of the United States fluctuates greatly,especially at the time nodes of major events.