A non-parametric method to investigate internal trends in time sequence: A case study of temperature and precipitation.

• A nonparametric trend testing method was proposed. • The statistical values of this method have asymptotic normality. • It tests not only overall but also internal trends in precipitation and temperature. Trend testing is essential for time sequence analysis. However, the existing trend testing methods mainly study the trends of the sequence as a whole, while there is a lack of feasible research tools for the internal trends of the sequence. Therefore, a non-parametric method was proposed to study the overall and internal trends of the sequence using the ideas of set pair, Cox-Stuart, Innovative Trend Analysis Methodology, and Mann-Kendall and applied to temperature and precipitation sequences. The applied study indicated that the overall and internal trends for global temperature were significantly increasing at the confidence level of α = 0.05. For precipitation, the trends (both overall and internal) of Laifeng and Leibo were increasing and decreasing, respectively, and some of the internal trends were significant (α = 0.05); however, the overall and internal trends of Pingbian and Sangzhi were not exactly the same, i.e., the trend of high (low) values in Pingbian (Sangzhi) was different from the other trends of the rest. In general, the method successfully tested not only the overall trends in temperature and precipitation, but also their internal (divided into low, middle, and high values) trends. These results agreed with the linear slope, Sen's slope, Mann-Kendall, and its improved. Therefore, the method can be used for trend analysis of the sequences. [ABSTRACT FROM AUTHOR]