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Cross-correlation between pairs of variables takes multi-time scale characteristic, and it can be totally different on different time scales (changing from positive correlation to negative one), e.g., the associations between mean air temperature and relative humidity over regions to the east of Taihang mountain in China. Therefore, how to correctly unveil these correlations on different time scales is really of great importance since we actually do not know if the correlation varies with scales in advance. Here, we compare two methods, i.e. Detrended Cross-Correlation Analysis (DCCA for short) and Pearson correlation, in quantifying scale-dependent correlations directly to raw observed records and artificially generated sequences with known cross-correlation features. Studies show that 1) DCCA related methods can indeed quantify scale-dependent correlations, but not Pearson method; 2) the correlation features from DCCA related methods are robust to contaminated noises, however, the results from Pearson method are sensitive to noise; 3) the scale-dependent correlation results from DCCA related methods are robust to the amplitude ratio between slow and fast components, while Pearson method may be sensitive to the amplitude ratio. All these features indicate that DCCA related methods take some advantages in correctly quantifying scale-dependent correlations, which results from different physical processes.

Quantifying distinct associations on different temporal scales: comparison of DCCA and Pearson methods