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Fundamental classes of ambit fields in space and space-time: theory, simulation and statistical inference

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Title: Fundamental classes of ambit fields in space and space-time: theory, simulation and statistical inference
Authors: Nguyen, Michele
Item Type: Thesis or dissertation
Abstract: With their origins in turbulence modelling, ambit fields have recently been presented as a new modelling framework. Since many subclasses studied in the literature have been restricted to the temporal setting, we focus on three classes of ambit fields in space and space-time: the spatio-temporal Ornstein-Uhlenbeck (STOU), the mixed STOU (MSTOU) and the volatility modulated moving average (VMMA) processes. Through the STOU and MSTOU processes, we examine how the spatio-temporal covariances of an ambit field are affected by our choice of the integration sets and the Lévy bases. Through the VMMA, we see how introducing stochastic volatility caters for spatial heteroskedasticity. That is, changing variances and covariances over space. In this thesis, we not only derive the theoretical properties of the models but also develop simulation and inference techniques. Discrete convolution approximations of the fields and compound Poisson approximations of the Lévy bases are used in the design of our simulation algorithms and the mean squared errors involved are derived. Moments-based methods are used for estimation and estimator properties such as consistency are established. In the case of a Gaussian STOU process, interval estimation is considered through pairwise composite likelihood methods and Monte Carlo confidence intervals. The practical relevance of our models is further illustrated using radiation anomaly and sea surface temperature anomaly data. The STOU, MSTOU and VMMA each capture a different, key aspect of the more general ambit field. It is hoped that by studying their theory, simulation and statistical inference methods, we can build a more holistic view of the general setting.
Content Version: Open Access
Issue Date: Jul-2017
Date Awarded: Dec-2017
URI: http://hdl.handle.net/10044/1/71305
DOI: https://doi.org/10.25560/71305
Copyright Statement: Creative Commons Attribution Non-Commercial No-Derivatives licence
Supervisor: Veraart, Almut E. D.
Pavliotis, Grigoris
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: 1396593
Department: Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Mathematics PhD theses



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