Detrended Partial Cross-correlation Analysis Of Three Nonstationary Time Series

There are a number of situations, ranging from natural science and social science, where different signals exhibit correlations in the presence of nonstationarity. The study on the long-range autocorrelations of time series and the long-range cross-correlation in the presence of nonstationarity between two time series have become the hot fields of recent research.We propose a new method--detrended partial cross-correlation analysis (DPCA), which is a generalization of detrended cross-correlation analysis (DCCA) and is based on partial correlation analysis, to quantify the partial cross-correlations of three simultaneously recorded time series in the presence of nonstationarity. This method is designed to investigate the cross correlation between two different simultaneously recorded time series after removing the effect of the third time series on each of them. We test the proposed DPCA method using the simulated data sets, which are generated with two different algorithms. Finally, we apply DPCA to investigate the partial cross-correlation of gold price, oil price and US dollar index, three different market indices respectively.