General correlation analysis: a new algorithm and application |
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| Authors: | Yu Zhou Qiang Zhang Vijay P Singh Mingzhong Xiao |
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| Institution: | 1.Department of Geography and Resource Management,The Chinese University of Hong Kong,Hong Kong,China;2.Department of Water Resources and Environment,Sun Yat-sen University,Guangzhou,China;3.School of Earth Sciences and Engineering,Suzhou University,Anhui,China;4.Key Laboratory of Water Cycle and Water Security in Southern China of Guangdong High Education Institute,Sun Yat-sen University,Guangzhou,China;5.Department of Biological & Agricultural Engineering and Department of Civil and Environmental Engineering,Texas A & M University,Texas,USA |
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| Abstract: | Correlation associations have been detected using Pearson’s r which aims to analyze linear correlation between two variables. It should be noted here that associations between hydro-meteorological variables are usually nonlinear. In this sense, the classical correlation analysis method cannot truly reflect the inherent associations between variables characterized by nonlinear associations. In this case, a new algorithm has been proposed by using the ideas of local correlation, detrended cross-correlation analysis and multifractals, and this novel algorithm is called as the general detrended correlation analysis. The newly-proposed algorithm was evaluated for the validity with numerically-generated time series and the real world hydrological series. The results indicate that the newly-proposed algorithm can well reflect the nonlinear and non stationary associations between two hydrological series when compared to the classical relation detection method such as the Pearson correlation analysis method, and it is particularly the case under the condition that hydrological abrupt changes of the hydrological processes occur where the classical association analysis is not appropriate. |
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