Statistical models for spatio-temporal extrema and dependencies
File(s)
Author(s)
Noven, Ragnhild Cassel
Type
Thesis
Abstract
This thesis develops statistical models for capturing the dependence characteristics and distributional structures of spatio-temporal data. In the first part we propose a parsimonious stochastic process model for characterising rainfall time series. It is shown that the model is sufficiently flexible to capture important features of the rainfall process at different locations and time scales. We also study an application to the pricing of rainfall derivatives that introduces the market price of risk via the Esscher transform, and calculate futures prices based on empirical rainfall data.
In the second part we consider statistical models based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. We discuss properties of this class and introduce a novel representation of trawl processes in terms of independent random variables.
The trawl process class is used to construct a new model for characterising temporal dependence in exceedances above a threshold, which has the proper limiting distribution from extreme value theory. We illustrate the model by applying it to time series of rainfall and pollution measurements, and demonstrate its ability to capture the dependence structure of extreme value data.
The third part of the thesis introduces a framework for hierarchical models based on trawl processes, which includes the extreme value model as a special case. We develop a targeted MCMC algorithm for this class of models, which exploits the trawl process representation from the second part. We also introduce two specific models in this framework, and fit the second model to a time series of wind production.
In the final part we consider a wider class of processes for spatio-temporal modelling, which contains the specific models considered previously. We discuss the construction of models with specific covariance functions, and introduce a discrete approximation for these processes.
In the second part we consider statistical models based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. We discuss properties of this class and introduce a novel representation of trawl processes in terms of independent random variables.
The trawl process class is used to construct a new model for characterising temporal dependence in exceedances above a threshold, which has the proper limiting distribution from extreme value theory. We illustrate the model by applying it to time series of rainfall and pollution measurements, and demonstrate its ability to capture the dependence structure of extreme value data.
The third part of the thesis introduces a framework for hierarchical models based on trawl processes, which includes the extreme value model as a special case. We develop a targeted MCMC algorithm for this class of models, which exploits the trawl process representation from the second part. We also introduce two specific models in this framework, and fit the second model to a time series of wind production.
In the final part we consider a wider class of processes for spatio-temporal modelling, which contains the specific models considered previously. We discuss the construction of models with specific covariance functions, and introduce a discrete approximation for these processes.
Version
Open Access
Date Issued
2016-07
Date Awarded
2016-12
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Veraart, Almut E.D.
Gandy, Axel
Sponsor
Imperial College London
European Union
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)