Functional time series forecasting of extreme values

Abstract

We consider forecasting functional time series of extreme values within a generalized extreme value distribution (GEV). The GEV distribution can be characterized 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 modeled 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 modeling 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.

KEYWORDs:

• Generalized extreme value distribution
• generalized additive extreme value model
• dimension reduction
• maximum daily temperature

Acknowledgments

The authors would like to acknowledge insightful comments from a reviewer which led to a much-improved article.

Funding

The first author acknowledges the financial support by the ANU College of Business and Economics Mid-Career Researcher Grant, and the second author acknowledges the financial support by the Research School of Finance, Actuarial Studies and Statistics Honours Scholarship.