Dissecting innovative trend analysis

Investigating the nature of trends in time series is one of the most common analyses performed in hydro-climate research. However, trend analysis is also widely abused and misused, often overlooking its underlying assumptions, which prevent its application to certain types of data. A mechanistic application of graphical diagnostics and statistical hypothesis tests for deterministic trends available in ready-to-use software can result in misleading conclusions. This problem is exacerbated by the existence of questionable methodologies that lack a sound theoretical basis. As a paradigmatic example, we consider the so-called Sen's 'innovative' trend analysis (ITA) and the corresponding formal trend tests. Reviewing each element of ITA, we show that (1) ITA diagrams are equivalent to well-known two-sample quantile-quantile (q-q) plots; (2) when applied to finite-size samples, ITA diagrams do not enable the type of trend analysis that it is supposed to do; (3) the expression of ITA confidence intervals quantifying the uncertainty of ITA diagrams is mathematically incorrect; and (4) the formulation of the formal tests is also incorrect and their correct version is equivalent to a standard parametric test for the difference between two means. Overall, we show that ITA methodology is affected by sample size, distribution shape, and serial correlation as any parametric technique devised for trend analysis. Therefore, our results call into question the ITA method and the interpretation of the corresponding empirical results reported in the literature.