Cross-correlations between the CSI300 index and commodity markets: Non-stationary principal component analysis (NSPCA)

The categorization of high dimensional data present a fascinating challenge to statistical models as frequent number of highly correlated dimensions or attributes can affect the accuracy of model. When the underlying time series present non-stationarity, typically when the series are contaminated by external trends, the strength of cross-correlations among variables is often overestimated or underestimated, and therefore, the traditional PCA method fails to rely on reliable cross-correlations to guide for the linear transformation of original variables. In this study, we apply the non-stationary principal component analysis (NSPCA) introduced by Zhao and Shang (2015) to analysis cross-correlations between the CSI300 Index and commodity markets. The main result of this paper is that for commodity markets, utilization of the non-stationary principal component analysis (NSPCA) can improve the efficiency, with more proportion of total population variance (information) due to an equal number of principal components than the traditional PCA. Meanwhile, as the increasing of time scales, this efficiency of NSPCA has a trend to increase. To check that whether the first several principal components can preserve some important information of original data or not, we apply detrended cross-correlation analysis (DCCA) to examine cross-correlation relationship between the CSI300 Index and the selected first five principal components and conclude that the information of long-range dependence measured by Hurst exponent has not been lost.