Functional time series forecasting of extreme values

Hanlin Shang*, Ruofan Xu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
18 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)182-199
Number of pages18
JournalCommunications in Statistics Case Studies Data Analysis and Applications
Issue number2
Early online date6 Jan 2021
Publication statusPublished - 8 Jun 2021


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


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