论文标题
功能时间序列预测极值
Functional time series forecasting of extreme values
论文作者
论文摘要
我们考虑在广义极值分布（GEV）内的预测功能时间序列。 GEV分布可以使用三个参数（位置，比例和形状）来表征。结果，可以通过预测这三个潜在参数来实现GEV密度的预测。根据基础数据结构的不同，这三个参数中的某些可以建模为标量或函数。我们提供两种预测算法来建模和预测这些参数。为了评估预测不确定性，我们应用了筛布方法来构造预测极值的指定和同时预测间隔。通过每日最高温度数据集说明，我们演示了将这些参数作为函数建模的优势。此外，在各种方案下，使用几个蒙特卡洛模拟数据来量化我们方法的有限样本性能。
We consider forecasting functional time series of extreme values within a generalised extreme value distribution (GEV). The GEV distribution can be characterised using the three parameters (location, scale and shape). As a result, the forecasts of the GEV density can be accomplished by forecasting these three latent parameters. Depending on the underlying data structure, some of the three parameters can either be modelled as scalars or functions. We provide two forecasting algorithms to model and forecast these parameters. To assess the forecast uncertainty, we apply a sieve bootstrap method to construct pointwise and simultaneous prediction intervals of the forecasted extreme values. Illustrated by a daily maximum temperature dataset, we demonstrate the advantages of modelling these parameters as functions. Further, the finite-sample performance of our methods is quantified using several Monte-Carlo simulated data under a range of scenarios.
