Properties of the Cox–Stuart Test for Trend in Application to Hydrological Series: The Simulation Study

Abstract

The size and power properties of the Cox–Stuart test for detection of a monotonic deterministic trend in hydrological time series are analyzed using the Monte Carlo method. The influence of distribution properties, lengths of series, and trend slopes is studied. Results indicate good size in all cases. The power is high for: length over 60 and strong trend slope, low or medium variation, and medium slope. The power declines if slope and length decrease and if variability increases. The properties are better for skewed distributions than for symmetrical. The test is slightly weaker in comparison to the Mann–Kendall test.

Keywords:

• Hydrological time series
• Power and size of a test
• Test for deterministic trend

Mathematics Subject Classification:

• 65C05
• 62P12