Assessing the Performance of Parametric and Non-Parametric Tests for Trend Detection in Partial Duration Time Series

The detection of non-stationarities in partial duration time series (or peak-over-threshold, POT) depends on a number of factors, including the length of the time series, the selected statistical test, and the heaviness of the tail of the distribution. Because of the more limited attention received in the literature when compared to the trend detection on block maxima variables, we perform a Monte Carlo simulation study to evaluate the performance of different approaches (Spearman’s rho (SP), Mann-Kendall test (MK), Ordinary Least Squared Regression (OLS), Sen’s slope estimator (SEN), and the non-stationary Generalized Pareto distribution fit (GPD_NS)) to identify the presence of trends in POT records characterized by different sample sizes (n), shape parameter and degrees of non-stationarity. We also estimate the probability of occurrence of Type S errors when using the OLS and SEN to determine the magnitude of trends. The results point to a power gain for all tests by increasing sample size and degree of non-stationarity. The same increased detection is noted when reducing the shape parameter (i.e., going from unbounded to bounded distributions). While the GPD_NS has the best performance overall, the OLS performs well when detecting trends for low or negative shape values. On the other hand, the use of a non-parametric test is recommended in samples with a high positive skew. Furthermore, the use of sampling rates greater than 1 (i.e., selecting more than just one event per year on average) to increase the POT sample size is encouraged, especially when dealing with small records. In this case, gains in power of detection and a reduction in the probability of type S error occurrence are observed, especially when the sampling rate ≤ 0 (i.e., unbounded distribution). Moreover, the use of SEN to estimate the magnitude of a trend is preferable over OLS due to its slightly smaller probability of occurrence of type S error when the shape parameter is positive.