Abstract
ABSTRACT The selection of an appropriate nonstationary Generalized Extreme Value (GEV) distribution is frequently based on methods, such as Akaike information criterion (AIC), second-order Akaike information criterion (AICc), Bayesian information criterion (BIC) and likelihood ratio test (LRT). Since these methods compare all GEV-models considered within a selection process, the hypothesis that the number of candidate GEV-models considered in such process affects its own outcomehas been proposed. Thus, this study evaluated the performance of these four selection criteria as function of sample sizes, GEV-shape parameters and different numbers candidate GEV-models. Synthetic series generated from Monte Carlo experiments and annual maximum daily rainfall amounts generated by the climate model MIROC5 (2006-2099; State of Sao Paulo-Brazil) were subjected to three distinct fitting processes, which considered different numbers of increasingly complex GEV-models. The AIC, AICc, BIC and LRT were used to select “the most appropriate” model for each series within each fitting process.BIC outperformed all other criteria when the synthetic series were generated from stationary GEV-models or from GEV-models allowing changes only in the location parameter (linear or quadratic). However, this latter method performed poorly when the variance of the series varied over time. In such cases, AIC and AICc should be preferred over BIC and LRT. The performance of all selection criteria varied with the different number of GEV-models considered in each fitting processes. In general, the higher the number of GEV-models considered within aselection process, the worse the performance of the selection criteria. In conclusion, the number of GEV-models to be used within a selection process should be set with parsimony.
Highlights
Changes in frequency and intensity of extreme hydrometeorological events have been observed in virtually all regions of the world (Alexander et al 2006; Fischer and Knutti 2015; Pereira et al 2018)
Akaike information criterion (AIC) and AICc should be preferred over Bayesian information criterion (BIC) and likelihood ratio test (LRT)
In order to provide information on this hypothesis, the goal of this study was to evaluate the performance of these four selection criteria (AIC, AICc, BIC and LRT) as function of different sample sizes (30 to 100), different GEVshape parameters (-0.50 to 0.50) and different numbers of increasingly complex Generalized Extreme Value (GEV)-models used within three different selection process
Summary
Changes in frequency and intensity of extreme hydrometeorological events have been observed in virtually all regions of the world (Alexander et al 2006; Fischer and Knutti 2015; Pereira et al 2018). It is widely accepted that models assessing the probability of extreme weather events (e.g. the Generalized Extreme Value (GEV) distribution) should account for the presence of nonstationarities, such as those associated with interannual or interdecadal climate variabilities or with the global warming (Parker et al 2007; Fischer and Knutti 2015). On such context, methods estimating the GEV-parameters under nonstationary conditions have been developed and used in several studies. Nonstationary GEV models (CDN-GEV) become capable of representing a wide range of linear and nonlinear relationships among covariates and the GEV-parameters (Cannon 2010)
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