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

Abstract

Abstract. 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.

Parametric Assessment of Trend Test Power in a Changing Environment

“…According to this criterion, the model with the lowest value of AIC should be the better one among the set of models examined. Following the idea of exploiting model selection criteria for detecting changes in time series analysis, Totaro et al [14] proposed the use of AIC R , defined as the ratio between the AIC values obtained, respectively, from nonstationary and stationary candidate models. They showed that, through Monte Carlo numerical experiments, is possible to evaluate AIC R statistical distribution and find the AIC R,α threshold value corresponding to an assigned level of significance α .…”

“…The need for giving an appropriate evaluation of the power of the MK test was highlighted, among others, by Totaro et al [14]. They followed the approach proposed by Yue et al [15] that produced a numerical evaluation of the MK test power for Generalized Extreme Value (GEV) distributed samples.…”

“…In environmental applications in particular, the length of the observed series required to reach an acceptable power value could be very different according to the variable's parent distribution and the strength of the trend [10,[14][15][16]. It could be much shorter for temperature and humidity time series than for runoff and precipitation time series that usually show higher space-time variability.…”

“…Following this path of investigation, Totaro et al [14] showed that both parametric and non-parametric tests for trend assessment suffer from the following issues: (i) the results of the test are dependent on the parent distribution and (ii) for weak trends, i.e., for small values of the trend coefficient, the test power reduces to low and unacceptable values.…”

“…The goals of this paper are (i) to further develop the use of parametric tests, based on model selection criteria (Akaike Information Criterion, AIC ∆ ) described in Section 2, (ii) to provide a generalized methodology which exploits a Rescaled GEV distributed variable, and (iii) to extend the evaluations performed by Totaro et al [14] to parameter ranges covering the variability of different physical variables suitable for climate change assessment. Such a development is of great practical interest because, in principle, it provides a general tool for estimating the power value and assesses the real statistical significance on extreme values of any variable of environmental interest.…”