A Nonparametric Trend Test for Seasonal Data With Serial Dependence

TLDR

Statistical tests for monotonic trend in seasonal hydrologic time series are confounded by nonnormality, missing values, seasonality, censoring, and serial dependence. This paper extends the Mann–Kendall test to handle such data. The rank‑based extension is robust to nonnormality, censoring, seasonality, and missing values, maintains correct type I error under most serial correlation scenarios except strong long‑term persistence or very short records, but is less powerful than a simpler non‑robust test when serial correlation is absent.

Abstract

Statistical tests for monotonic trend in seasonal (e.g., monthly) hydrologic time series are commonly confounded by some of the following problems: nonnormal data, missing values, seasonality, censoring (detection limits), and serial dependence. An extension of the Mann‐Kendall test for trend (designed for such data) is presented here. Because the test is based entirely on ranks, it is robust against nonnormality and censoring. Seasonality and missing values present no theoretical or computational obstacles to its application. Monte Carlo experiments show that, in terms of type I error, it is robust against serial correlation except when the data have strong long‐term persistence (e.g., ARMA (1, 1) monthly processes with ϕ > 0.6) or short records (∼ 5 years). When there is no serial correlation, it is less powerful than a related simpler test which is not robust against serial correlation.