Multivariate overall and dependence trend tests, applied to hydrology.

Given climate change, trend detection is gaining increasing attention in the context of multivariate frequency analysis. In this paper, we propose new statistical tests for multivariate trend detection. The first one, a multivariate overall trend (MOT) test, is designed to detect trend in all components of the multivariate distribution (margins and dependence structure) whereas the second test is a multivariate dependence trend (MDT) test focusing on detecting trend in the dependence structure. A simulation study is used to evaluate the performance of the proposed tests. Results show that the proposed MOT test performs well when trend is present in margins, in the dependence structure and/or in both. Likewise, results of the proposed MDT test indicate a higher power when the trend is in the dependence structure. Moreover, an application to a real-world dataset is provided. Performing the proposed tests with the univariate tests provides a complete overview of trend detection. • Two multivariate trend tests for multivariate hydrological series are proposed. • New multivariate overall trend (MOT) test dealing with trend in all the components of the whole multivariate distribution. • New multivariate dependence trend (MDT) test focuses on trend in the dependence structure. • Vast simulation study is considered to evaluate the performance of the tests. • The developed tests show high performance, with increasing power observed as the trend slope and sample size increase. [ABSTRACT FROM AUTHOR]