General correlation analysis: a new algorithm and application

2014, Springer-Verlag Berlin Heidelberg. Correlation associations have been detected using Pearsons 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.

General correlation analysis: a new algorithm and application Academic Article