Statistics

Mathematical analysis

Econometrics

Geotechnical engineering

Variance (accounting)

Distribution (mathematics)

Series (stratigraphy)

Geometry

Scaling

Normal distribution

Accounting

Geology

Business

Mathematics

Statistical hypothesis testing

Estimator

Persistence (discontinuity)

Paleontology

Hydrological Sciences Journal

The existence of persistence contaminates the results of the Mann-Kendall (MK) trend test. This paper proposes an improved MK test for hydrological data with both positive and negative persistence. To this end, the variance and distribution patterns of S were modified under the scaling hypothesis. Different estimators of the scaling coefficient were compared. According to the results, the generalized normal distribution is the best approximation to fit the exact distribution of S with both positive and negative persistence. The centred detrending moving average was demonstrated to be the best estimator of the scaling coefficient for series with a trend. The improved MK test was proven to be more advantageous than other trend detection methods for the synthetic time series and observed precipitation data obtained from nine hydrometric stations located in China. With this modification, the application of the MK test can be extended to long-term persistent data.

Modified Mann-Kendall trend test for hydrological time series under the scaling hypothesis and its application