Correlation Coefficient‐Based Information Criterion for Quantification of Dependence Characteristics in Hydrological Time Series

Abstract

AbstractQuantification of the dependence characteristics in hydrological time series is essential for understanding hydrological variability and for managing water resources. However, how determining a suitable model for describing the dependent components is still a challenge. In this article, we proposed a correlation coefficient‐based information criterion (CCIC) to determine the optimal model order of regression‐based models for quantifying the dependence characteristics in hydrological time series. CCIC was developed by combining the index of correlation coefficient and the information entropy index. The former was used to reflect the fitting error of the model and the latter was used as a penalty term to reflect the model uncertainty. They have similar roles as the two terms of the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) used commonly in hydrology. Results of Monte‐Carlo experiments verified higher and more stable accuracy of determining the true model order by CCIC than by AIC and BIC. Moreover, results indicated that the mean value of a time series had a big impact on the accuracy of CCIC. If the mean value of a time series was far from its initial value, the estimation of CCIC would have a big bias, causing low accuracy in the determination of suitable model order. The application of CCIC to annual precipitation from 520 stations in China further confirmed its advantages over AIC and BIC and indicated the significant short‐term dependence characteristics of annual precipitation in the Yangtze River basin. The proposed CCIC approach has potential for wider use in hydrometeorology.