A framework of change-point detection for multivariate hydrological series

Abstract

Under changing environments, not only univariate but also multivariate hydrological series might become nonstationary. Nonstationarity, in forms of change-point or trend, has been widely studied for univariate hydrological series, while it attracts attention only recently for multivariate hydrological series. For multivariate series, two types of change-point need to be distinguished, i.e., change-point in marginal distributions and change-point in the dependence structure among individual variables. In this paper, a three-step framework is proposed to separately detect two types of change-point in multivariate hydrological series, i.e., change-point detection for individual univariate series, estimation of marginal distributions, and change-point detection for dependence structure. The last step is implemented using both the Cramér-von Mises statistic (CvM) method and the copula-based likelihood-ratio test (CLR) method. For CLR, three kinds of copula model (symmetric, asymmetric, and pair-copula) are employed to construct the dependence structure of multivariate series. Monte Carlo experiments indicate that CLR is far more powerful than CvM in detecting the change-point of dependence structure. This framework is applied to the trivariate flood series composed of annual maxima daily discharge (AMDD), annual maxima 3 day flood volume, and annual maxima 15 day flood volume of the Upper Hanjiang River, China. It is found that each individual univariate flood series has a significant change-point; and the trivariate series presents a significant change-point in dependence structure due to the abrupt change in the dependence structure between AMDD and annual maxima 3 day flood volume. All these changes are caused by the construction of the Ankang Reservoir.