Abstract
In this paper, a new method, detrended partial-cross-correlation analysis (DPCCA), is proposed. Based on detrended cross-correlation analysis (DCCA), this method is improved by including partial-correlation technique, which can be applied to quantify the relations of two non-stationary signals (with influences of other signals removed) on different time scales. We illustrate the advantages of this method by performing two numerical tests. Test I shows the advantages of DPCCA in handling non-stationary signals, while Test II reveals the “intrinsic” relations between two considered time series with potential influences of other unconsidered signals removed. To further show the utility of DPCCA in natural complex systems, we provide new evidence on the winter-time Pacific Decadal Oscillation (PDO) and the winter-time Nino3 Sea Surface Temperature Anomaly (Nino3-SSTA) affecting the Summer Rainfall over the middle-lower reaches of the Yangtze River (SRYR). By applying DPCCA, better significant correlations between SRYR and Nino3-SSTA on time scales of 6 ~ 8 years are found over the period 1951 ~ 2012, while significant correlations between SRYR and PDO on time scales of 35 years arise. With these physically explainable results, we have confidence that DPCCA is an useful method in addressing complex systems.
Highlights
In this paper, a new method, detrended partial-cross-correlation analysis (DPCCA), is proposed
Based on detrended cross-correlation analysis (DCCA), this method is improved by including partial-correlation technique, which can be applied to quantify the relations of two non-stationary signals on different time scales
Where FDCCA is the fluctuation function obtained fromÈDCÉCAÈ18,ÉFDFA is the fluctuation function obtained from DFA20, and xi[1 ], xi2 are the two considered time series, one can quantify the level of crosscorrelations on different time scales
Summary
A new method, detrended partial-cross-correlation analysis (DPCCA), is proposed. By applying TCA to the two records, the calculated correlation coefficient is only 0519, which is not statistically significant according to the student’s t-test To explain this low correlation coefficient, one reason could be that the connection between SRYR and Nino3-SSTA is nonstationary over time. The low (high) pass frequency, or the band-width are usually chosen subjectively, which make these simple filter methods not appropriate in performing cross-correlation research over different time scales Another method, cross-spectral analysis (CSA)[16,17], may be useful in discussing connections of two time series on different time scales, but it requires the analyzed data to be stationary with no external trends, which are rare in nature. We will mainly focus on the DCCA cross-correlation coefficient rDCCA derived from DCCA
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