Time series and extreme value analyses are two statistical approaches usually applied to study hydrological data. Classical techniques, such as ARIMA models (in the case of mean flow predictions), and parametric generalised extreme value (GEV) fits and nonparametric extreme value methods (in the case of extreme value theory) have been usually employed in this context. In this paper, nonparametric functional data methods are used to perform mean monthly flow predictions and extreme value analysis, which are important for flood risk management. These are powerful tools that take advantage of both, the functional nature of the data under consideration and the flexibility of nonparametric methods, providing more reliable results. Therefore, they can be useful to prevent damage caused by floods and to reduce the likelihood and/or the impact of floods in a specific location. The nonparametric functional approaches are applied to flow samples of two rivers in the U.S. In this way, monthly mean flow is predicted and flow quantiles in the extreme value framework are estimated using the proposed methods. Results show that the nonparametric functional techniques work satisfactorily, generally outperforming the behaviour of classical parametric and nonparametric estimators in both settings.

翻译：时间序列分析和极值分析是研究水文数据的两种常用统计方法。经典技术，如ARIMA模型（用于平均流量预测）、参数化广义极值（GEV）拟合和非参数化极值方法（用于极值理论），在此背景下常被采用。本文使用非参数函数数据方法进行月平均流量预测和极值分析，这对洪水风险管理至关重要。这些方法利用了所考虑数据的函数性质和非参数方法的灵活性，是强大的工具，能提供更可靠的结果。因此，它们有助于预防洪水造成的损害，并降低特定地点洪水的发生概率和/或影响。非参数函数方法应用于美国两条河流的流量样本。通过这种方式，使用所提出的方法预测月平均流量，并在极值框架下估计流量分位数。结果显示，非参数函数技术表现令人满意，通常在这两种情境下优于经典参数化和非参数化估计器的性能。