Functional time series forecasting of extreme values

TL;DR

This paper develops methods for forecasting extreme values in functional time series using GEV distribution parameters, incorporating bootstrap-based uncertainty quantification, and demonstrates advantages through temperature data analysis and simulations.

Contribution

It introduces two novel algorithms for forecasting GEV parameters in functional data, with a focus on modeling parameters as functions and assessing forecast uncertainty.

Findings

Modeling parameters as functions improves forecast accuracy.

Bootstrap methods effectively quantify forecast uncertainty.

Methods perform well in simulations and temperature data applications.

Abstract

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.