Statistical Modelling 24 (2) (2024), 169193
A model for space-time threshold exceedances
with an application to extreme rainfall
Paola Bortot,
Dipartimento di Scienze Statistiche,
Universit̀ di Bologna,
Italy.
Carlo Gaetan,
Dipartimento di Scienze Ambientali,
Informatica e Statistica,
Universit̀ Ca’ Foscari,
Venezia,
Italy.
e-mail: gaetan@unive.it
Abstract:
In extreme value studies, models for observations exceeding a fixed high threshold have the
advantage of exploiting the available extremal information while avoiding bias from low values. In the
context of space-time data, the challenge is to develop models for threshold exceedances that account
for both spatial and temporal dependence. We address this issue through a modelling approach that
embeds spatial dependence within a time series formulation. The model allows for different forms of
limiting dependence in the spatial and temporal domains as the threshold level increases. In particular,
temporal asymptotic independence is assumed, as this is often supported by empirical evidence, especially
in environmental applications, while both asymptotic dependence and asymptotic independence
are considered for the spatial domain. Inference from the observed exceedances is carried out through
a combination of pairwise likelihood and a censoring mechanism. For those model specifications for
which direct maximization of the censored pairwise likelihood is unfeasible, we propose an indirect
inference procedure which leads to satisfactory results in a simulation study. The approach is applied
to a dataset of rainfall amounts recorded over a set of weather stations in the North Brabant province
of the Netherlands. The application shows that the range of extremal patterns that the model can cover
is wide and that it has a competitive performance with respect to an alternative existing model for
space-time threshold exceedances.
Keywords:
asymptotic dependence, asymptotic independence, Gaussian spatial process, indirect inference,
max-stable process, Student’s t-spatial process
Downloads:
Data and Code in zipped archive, supplementary material as PDF.
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