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Title: Fundamental classes of ambit fields in space and space-time : theory, simulation and statistical inference
Author: Nguyen, Michele
ISNI:       0000 0004 7963 7126
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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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.
Supervisor: Veraart, Almut E. D. ; Pavliotis, Grigoris Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral