Appropriate model selection methods for nonstationary generalized extreme value models

Several evidences of hydrologic data series being nonstationary in nature have been found to date. This has resulted in the conduct of many studies in the area of nonstationary frequency analysis. Nonstationary probability distribution models involve parameters that vary over time. Therefore, it is not a straightforward process to apply conventional goodness-of-fit tests to the selection of an appropriate nonstationary probability distribution model. Tests that are generally recommended for such a selection include the Akaike's information criterion (AIC), corrected Akaike's information criterion (AICc), Bayesian information criterion (BIC), and likelihood ratio test (LRT). In this study, the Monte Carlo simulation was performed to compare the performances of these four tests, with regard to nonstationary as well as stationary generalized extreme value (GEV) distributions. Proper model selection ratios and sample sizes were taken into account to evaluate the performances of all the four tests. The BIC demonstrated the best performance with regard to stationary GEV models. In case of nonstationary GEV models, the AIC proved to be better than the other three methods, when relatively small sample sizes were considered. With larger sample sizes, the AIC, BIC, and LRT presented the best performances for GEV models which have nonstationary location and/or scale parameters, respectively. Simulation results were then evaluated by applying all four tests to annual maximum rainfall data of selected sites, as observed by the Korea Meteorological Administration.