Modelling the tails of distributions is important in many fields, such as environmental science, hydrology, insurance, engineering and finance, where the risk of unusually large or small events are of interest. This thesis applies extreme value models in neonatal and finance studies and develops novel extreme value modelling for financial applications, to overcome issues associated with the dependence induced by volatility clustering and threshold choice. The instability of preterm infants stimulates the interests in estimating the underlying variability of the physiology measurements typically taken on neonatal intensive care patients. The stochastic volatility model (SVM), fitted using Bayesian inference and a particle filter to capture the on-line latent volatility of oxygen concentration, is used in estimating the variability of medical measurements of preterm infants to highlight instabilities resulting from their under-developed biological systems. Alternative volatility estimators are considered to evaluate the performance of the SVM estimates, the results of which suggest that the stochastic volatility model provides a good estimator of the variability of the oxygen concentration data and therefore may be used to estimate the instantaneous latent volatility for the physiological measurements of preterm infants. The classical extreme value distribution, generalized pareto distribution (GPD), with the peaks-over-threshold (POT) method to ameliorate the impact of dependence in the extremes to infer the extreme quantile of the SVM based variability estimates. Financial returns typically show clusters of observations in the tails, often termed “volatility clustering” which creates challenges when applying extreme value models, since classical extreme value theory assume independence of underlying process. Explicit modelling on GARCH-type dependence behaviour of extremes is developed by implementing GARCH conditional variance structure via the extreme value model parameters. With the combination of GEV and GARCH models, both simulation and empirical results show that the combined model is better suited to explain the extreme quantiles. Another important benefit of the proposed model is that, as a one stage model, it is advantageous in making inferences and accounting for all uncertainties much easier than the traditional two stage approach for capturing this dependence. To tackle the challenge threshold choice in extreme value modelling and the generally asymmetric distribution of financial data, a two tail GPD mixture model is proposed with Bayesian inference to capture both upper and lower tail behaviours simultaneously. The proposed two tail GPD mixture modelling approach can estimate both thresholds, along with other model parameters, and can therefore account for the uncertainty associated with the threshold choice in latter inferences. The two tail GPD mixture model provides a very flexible model for capturing all forms of tail behaviour, potentially allowing for asymmetry in the distribution of two tails, and is demonstrated to be more applicable in financial applications than the one tail GPD mixture models previously proposed in the literature. A new Value-at-Risk (VaR) estimation method is then constructed by adopting the proposed mixture model and two-stage method: where volatility estimation using a latent volatility model (or realized volatility) followed by the two tail GPD mixture model applied to independent innovations to overcome the key issues of dependence, and to account for the uncertainty associated with threshold choice. The proposed method is applied in forecasting VaR for empirical return data during the current financial crisis period.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-09-06T17:26:12Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação Mestrado- Carlos Eduardo Castor de Melo.pdf: 2325318 bytes, checksum: 1a456db1f76d03f35cc83b12a6026b6b (MD5) / Made available in DSpace on 2016-09-06T17:26:12Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação Mestrado- Carlos Eduardo Castor de Melo.pdf: 2325318 bytes, checksum: 1a456db1f76d03f35cc83b12a6026b6b (MD5) Previous issue date: 2015-08-27 / FACEPE / análise da similaridade entre algoritmos de aprendizagem de máquina é um importante aspecto na área de Meta-Aprendizado, onde informações obtidas a partir de processos de aprendizagem conhecidos podem ser utilizadas para guiar a seleção de algoritmos para tratar novos problemas apresentados. Essa similaridade é geralmente calculada através de métricas globais de desempenho, que omitem informações importantes para o melhor entendimento do comportamento dos algoritmos. Também existem abordagens onde é verificado o desempenho individualmente em cada instância do problema. Ambas as abordagens não consideram os custos associados a cada classe do problema, negligenciando informações que podem ser muito importantes em vários contextos de aprendizado. Nesse trabalho são apresentadas métricas para a avaliação do desempenho de algoritmos em cenários sensíveis a custo. Cada cenário é descrito a partir de um método para escolha de limiar para a construção de um classificador a partir de um modelo aprendido. Baseado nos valores de desempenho em cada instância, é proposta uma forma de avaliar a similaridade entre os algoritmos tanto em nível de problema como em nível global. Os experimentos realizados para ilustrar as métricas apresentadas neste trabalho foram realizados em um estudo de Meta-Aprendizado utilizando 19 algoritmos para a classificação das instâncias de 152 problemas. As medidas de similaridades foram utilizadas para a criação de agrupamentos hierárquicos. Os agrupamentos criados mostram como o comportamento entre os algoritmos diversifica de acordo com o cenário de custo a ser tratado. / The analysis of the similarity between machine learning algorithms is an important aspect of Meta-Learning, where knowledge gathered from known learning processes can be used to guide the selection of algorithms to tackle new learning problems presented. This similarity is usually calculated through global performance metrics that omit important information about the algorithm behavior. There are also approaches where the performance is verified individually on each instance of a problem. Both these approaches do not consider the costs associated with each problem class, hence they neglect information that can be very important in different learning contexts. In this study, metrics are presented to evaluate the performance of algorithms in cost sensitive scenarios. Each scenario is described by a threshold choice method, used to build a crisp classifier from a learned model. Based on the performance values for each problem instance, it is proposed a method to measure the similarity between the algorithms in a local level (for each problem) and in a global level (across all problems observed). The experiments used to illustrate the metrics presented in this paper were performed in a Meta-Learning study using 19 algorithms for the classification of the instances of 152 learning problems. The similarity measures were used to create hierarchical clusters. The clusters created show how the behavior of the algorithms diversifies according to the cost scenario to be treated.