Numerical investigation on the power of parametric and nonparametric tests for trend detection in annual maximum series

The need to fit time series characterized by the presence of a trend or change points has generated increased interest in the investigation of nonstationary probability distributions in recent years. Considering that the available hydrological time series can be recognized as the observable part of a stochastic process with a definite probability distribution, two main topics can be tackled in this context: the first is related to the definition of an objective criterion for choosing whether the stationary hypothesis can be adopted, whereas the second regards the effects of nonstationarity on the estimation of distribution parameters and quantiles for an assigned return period and flood risk evaluation. Although the time series trend or change points are usually detected using nonparametric tests available in the literature (e.g., Mann-Kendall or CUSUM test), the correct selection of the stationary or nonstationary probability distribution is still required for design purposes. In this light, the focus is shifted toward model selection criteria; this implies the use of parametric methods, including all of the issues related to parameter estimation. The aim of this study is to compare the performance of parametric and nonparametric methods for trend detection, analyzing their power and focusing on the use of traditional model selection tools (e.g., the Akaike information criterion and the likelihood ratio test) within this context. The power and efficiency of parameter estimation, including the trend coefficient, were investigated via Monte Carlo simulations using the generalized extreme value distribution as the parent with selected parameter sets.