Comparison of tests for trend in location and scale parameters in hydrological and precipitation time series

Abstract

Aim of the study: The objective was the comparison of properties of tests for trend in location and scale parameters for hydrological and precipitation time series, in particular (i) to review the non-parametric tests known from literature for various trends; the tests were studied from the point of view of their ability of detecting the existing trend (their power), (ii) to study the non-parametric tests for change in scale the power of which has not been estimated yet in application to hydrological and precipitation series (the Ansari-Bradley (AB), Siegel-Tukey (ST), Mood (M) tests), and (iii) to assess the differences between the tests. Material and methods: The study was based on the series of pseudo-numbers and on realizations of historical hydrological and precipitation time series. The Monte Carlo simulations and comparison of properties of the tests (AB, ST, M) that have not been studied yet in application to hydrological and precipitation series were conducted. The tests known in literature from applications in hydrological and precipitation series methods were also compared. Results and conclusions: Results show an increase of the power of the AB, ST and M tests with sample length and with strength of the step trend in scale, insensitivity to changes in the coefficient of variation, a low sensitivity to changes in type of the distribution, and the highest power of the M test. The step trend in scale in two exemplary series were identified. The AB, ST, and M tests can be applied to verify the hypothesis about step trend in scale in hydrological or precipitation time series.

Keywords

• hydrological and precipitation time series
• monotonic or step trend in location or scale parameter
• statistical test
• power of the test