Dissertations / Theses on the topic 'Peaks over threshold method'

Value-at-Risk (VaR) has long been the standard risk measure in financial risk management. However, VaR suffers from critical shortcomings as a risk measure when it comes to quantifying the most severe risks, which was made especially apparent during the financial crisis of 2007–2008. An alternative risk measure addressing the shortcomings of VaR known as expected shortfall (ES) is gaining popularity and is set to replace VaR as the standard measure of financial risk. This thesis introduces how extreme value theory can be applied in estimating ES using an unconditional peaks-over-threshold method. This includes giving an introduction to the theoretical foundations of the method. An application of this method is also performed on five different assets. These assets are chosen to serve as a proxy for the more broad asset classes of equity, fixed income, currencies, commodities and cryptocurrencies. In terms of ES, we find that cryptocurrencies is the riskiest asset and fixed income the safest.

Tendo em vista o crescente investimento em atividades economicamente importantes nas zonas costeiras, tal como a produção petrolífera brasileira e o crescimento na atividade portuária e esforço de pesca, a compreensão adequada dos fenômenos oceanográficos e meteorológicos sobre tais zonas é de grande valia para as operações desses setores. Os ventos representam um importante parâmetro para análise nesse sentido, sendo a principal fonte de energia para a geração de ondas de gravidade nos oceanos, e determinantes na caracterização de condições severas tempo. Uma série de estudos foram desenvolvidos nos últimos anos envolvendo a análise do comportamento dos extremos de ondas sobre a região do Oceano Atlântico Sul, de acordo com o crescimento da demanda por tais informações pelo setor industrial. No entanto, há poucos registros de estudos que caracterizem os extremos de intensidade de vento sobre essa região. E, em nenhum desses trabalhos, a separação direcional do vento extremo e seus fenômenos causadores foram levados em consideração. Dessa forma, o presente trabalho visa atender diretamente a necessidade por trabalhos nesse sentido para a região do Oceano Atlântico Sul, buscando oferecer uma análise dos campos de ventos extremos direcionalmente segregados, através de dados do projeto de reanálise \\textit{NCEP/NCAR Reanalysis I} e de resultados de uma simulação numérica com o modelo BRAMS. A tais conjuntos de dados foi aplicada a metodologia de análise de extremos \\textit{Peaks Over Threshold} (POT), que trata do ajuste dos excessos acima de um limiar estabelecido a uma distribuição conhecida, a Distribuição Generalizada de Pareto (Generalized Pareto Distribution - GPD). E, a partir disso, construir mapas com os valores extremos de retorno para longos períodos. Tais parâmetros são muito importantes na predição de eventos extremos e no refinamento de simulações de longo período. Os extremos relacionados aos fenômenos em larga escala, dados pelos campos do NCEP, em conjunto com o maior detalhamento em mesoescala, dado pelo BRAMS, refletiram diretamente no comportamento dos valores extremos de retorno. Para todas as direções do vento analisadas, observaram-se feições mais refinadas dos extremos de retorno para os resultados com a simulação do BRAMS, principalmente nas zonas costeiras. Essas feições, principalmente àquelas ao sul e sudeste do Oceano Atlântico Sul, tiveram seus valores potencializados em zonas já conhecidas na bibliografia pela grande incidência de eventos altamente energéticos.<br>Given the growing investment in important economic activities in coastal areas, such as oil and gas exploitation, harbor activities and increasing fishing effort, the proper understanding of oceanographic and meteorological phenomena over such areas has great value to the operations of such sectors. The winds are an important parameter for analysis in this context, being the main source of energy for gravity waves generation in the ocean, and determining the characterization of severe weather conditions. A number of studies have been developed in recent years involving the behavior of extreme waves over the South Atlantic Ocean region, given the rowing demand for such information by industrial sectors. However, there are few records of studies that characterize the extremes of wind speed fields over this region. And, in none of these works, the direction of the extreme wind and meteorological phenomenon associated were considered. Thus, this paper aims to address directly the need for work in this context for the South Atlantic Ocean region, seeking to offer an analysis of extreme wind fields directionally separated, through data from the NCEP/NCAR Reanalysis 1 and results from a numerical simulation with BRAMS. The Peaks Over Threshold (POT), which deals with the adjustment of the excesses above a threshold to the Generalized Pareto Distribution (GPD), was applied to both datasets. And from that, maps with the extreme return values have been developed for long return periods. These parameters are very important in predicting extreme events and refinement of long-period simulations. Extreme winds related to the large scale phenomena, represented by NCEP fields, in conjunction with the greater mesoscale detail, given by the BRAMS simulation, directly reflected in the behavior of extreme return values. For all wind directions analyzed, there were more refined features of the extremes return levels given by the BRAMS simulation, especially in coastal areas. These features, notably those in the south and southeast of the South Atlantic Ocean, values were strengthened in areas already known in the literature for the high incidence of energetic events.

One of today’s financial trends is securitization. Evaluating Securitization risk requires some strong quantitative skills and a deep understanding of both credit and market risk. For international securitization programs it is mandatory to take into account the exchange-rates-related risks. We will see the di˙erent methods to evaluate extreme variations of the exchange rates using the Extreme Value Theory and Monte Carlo simulations.<br>Värdepapperisering är en av dagens finansiella trender. Att utvärdera vär-depapperisering risk kräver starka kvantitativa kunskaper och en förståelseför både kredit- och marknadsrisk. För internationell värdepapperisering ärdet obligatoriskt att hänsyn tas till valutarisker. Vi kommer att se de olika metoder för att utvärdera extrema variationer i valutakurser med hjälp av extremvärdesteori och Monte Carlo-simuleringar.

The peaks over threshold (POT) method provides an attractive framework for estimating the risk of extreme events such as severe storms or large insurance claims. However, the conventional POT procedure, where the threshold excesses are modelled by a generalized Pareto distribution, suffers from small samples and subjective threshold selection. In recent years, two alternative approaches have been proposed in the form of mixture models that estimate the threshold and a folding procedure that generates larger tail samples. In this paper the empirical performances of the conventional POT procedure, the folding procedure and a mixture model are compared by modelling data sets on fire insurance claims and hurricane damage costs. The results show that the folding procedure gives smaller standard errors of the parameter estimates and in some cases more stable quantile estimates than the conventional POT procedure. The mixture model estimates are dependent on the starting values in the numerical maximum likelihood estimation, and are therefore difficult to compare with those from the other procedures. The conclusion is that none of the procedures is overall better than the others but that there are situations where one method may be preferred.

My dissertation is based on a unified self-consistent scaling framework which is consistent with key behavior exhibited by many spatially/temporally varying earth, environmental and other variables. This behavior includes tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that often decay with lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags, with breakdown in power-law scaling at small and/or large lags; linear relationships between log structure functions of successive orders at all lags, also known as extended self-similarity; and nonlinear scaling of structure function power-law exponents with function order. The major question we attempt to answer is: given data measured on a given support scale at various points throughout a 1D/2D/3D sampling domain, which appear to be statistically distributed and to scale in a manner consistent with that scaling framework, what can be said about the spatial statistics and scaling of its extreme values, on arbitrary separation or domain scales? To do so, we limit our investigation in 1D domain for simplicity and generate synthetic signals as samples from 1D sub-Gaussian random fields subordinated to truncated monofractal fractional Brownian motion (tfBm) or truncated fractional Gaussian noise (tfGn). Such sub-Gaussian fields are scale mixtures of stationary Gaussian fields with random variances that we model as being log-normal or Lévy α/2-stable. This novel interpretation of the data allows us to obtain maximum likelihood estimates of all parameters characterizing the underlying truncated sub-Gaussian fields. Based on synthetic data, we find these samples conform to the aforementioned scaling framework and confirm the effectiveness of generation schemes. We numerically investigate the manner in which variables, which scale according to the above scaling framework, behave at the tails of their distributions. Ours is the first study to explore the statistical scaling of extreme values, specifically peaks over thresholds or POTs, associated with such families of sub-Gaussian fields. Before closing this work, we apply and verify our analysis by investigating the scaling of statistics characterizing vertical increments in neutron porosity data, and POTs in absolute increments, from six deep boreholes in three different depositional environments.

<p>The work presented in this thesis studies the load and loadeffects of traffic loads on railway bridges. The increasedknowledge of the traffic loads, simulated using fieldmeasurements of actual trains, are employed in a reliabilityanalysis in an attempt at upgrading existing railwaybridges.</p><p>The study utilises data from a weigh-in-motion site whichrecords, for each train, the train speed, the loads from eachaxle and the axle spacings. This data of actual trainconfigurations and axle loads are portrayed as moving forcesand then used in computer simulations of trains crossing twodimensional simply supported bridges at constant speed. Onlysingle track short to medium span bridges are considered in thethesis. The studied load effect is the moment at mid-span. Fromthe computer simulations the moment history at mid-span isobtained.</p><p>The load effects are analysed by two methods, the first isthe classical extreme value theory where the load effect ismodelled by the family of distributions called the generalisedextreme value distribution (GEV). The other method adopts thepeaks-over-threshold method (POT) where the limiting family ofdistributions for the heights to peaks-over-threshold is theGeneralised Pareto Distribution (GPD). The two models aregenerally found to be a good representation of the data.</p><p>The load effects modelled by either the GEV or the GPD arethen incorporated into a reliability analysis in order to studythe possibility of raising allowable axle loads on existingSwedish railway bridges. The results of the reliabilityanalysis show that they are sensitive to the estimation of theshape parameter of the GEV or the GPD.</p><p>While the study is limited to the case of the ultimate limitstate where the effects of fatigue are not accounted for, thefindings show that for the studied cases an increase inallowable axle load to 25 tonnes would be acceptable even forbridges built to the standards of 1940 and designed to LoadModel A of that standard. Even an increase to both 27.5 and 30tonnes appears to be possible for certain cases. It is alsoobserved that the short span bridges ofapproximately fourmetres are the most susceptible to a proposed increase inpermissible axle load.</p><p><b>Keywords:</b>bridge, rail, traffic load, load effect,dynamic amplification factor, extreme value theory,peaks-over-threshold, reliability theory, axle loads, fielddata.</p>

Cette thèse a pour but le développement de certains aspects de la modélisation de la dépendance dans la gestion des risques en dimension plus grande que un. Le premier chapitre est constitué d'une introduction générale. Le deuxième chapitre est constitué d'un article s'intitulant " Estimating Bivariate Tail : a copula based approach ", soumis pour publication. Il concerne la construction d'un estimateur de la queue d'une distribution bivariée. La construction de cet estimateur se fonde sur une méthode de dépassement de seuil (Peaks Over Threshold method) et donc sur une version bivariée du Théorème de Pickands-Balkema-de Haan. La modélisation de la dépendance est obtenue via la Upper Tail Dependence Copula. Nous démontrons des propriétés de convergence pour l'estimateur ainsi construit. Le troisième chapitre repose sur un article: " A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation", soumis pour publication. Nous abordons le problème de l'extension de mesures de risque classiques, comme la Value-at-Risk et la Conditional-Tail-Expectation, dans un cadre multidimensionnel en utilisant la fonction de Kendall multivariée. Enfin, dans le quatrième chapitre de la thèse, nous proposons un estimateur des courbes de niveau d'une fonction de répartition bivariée avec une méthode plug-in. Nous démontrons des propriétés de convergence pour les estimateurs ainsi construits. Ce chapitre de la thèse est lui aussi constitué d'un article, s'intitulant " Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory", accepté pour publication dans la revue ESAIM:Probability and Statistics.

Le fonctionnement d'un système, de façon générale, peut être affecté par un incident imprévu. Lorsque cet incident a de lourdes conséquences tant sur l'intégrité du système que sur la qualité de ses produits, on dit alors qu'il se situe dans le cadre des événements dits extrêmes. Ainsi, de plus en plus les chercheurs portent un intérêt particulier à la modélisation des événements extrêmes pour diverses études telles que la fiabilité des systèmes et la prédiction des différents risques pouvant entraver le bon fonctionnement d'un système en général. C'est dans cette optique que s'inscrit la présente thèse. Nous utilisons la Théorie des Valeurs Extrêmes (TVE) et les statistiques d'ordre extrême comme outil d'aide à la décision dans la modélisation et la gestion des risques dans l'usinage et l'aviation. Plus précisément, nous modélisons la surface de rugosité de pièces usinées et la fiabilité de l'outil de coupe associé par les statistiques d'ordre extrême. Nous avons aussi fait une modélisation à l'aide de l'approche dite du "Peaks-Over Threshold, POT" permettant de faire des prédictions sur les éventuelles victimes dans l'Aviation Générale Américaine (AGA) à la suite d'accidents extrêmes. Par ailleurs, la modélisation des systèmes soumis à des facteurs d'environnement ou covariables passent le plus souvent par les modèles à risque proportionnel basés sur la fonction de risque. Dans les modèles à risque proportionnel, la fonction de risque de base est généralement de type Weibull, qui est une fonction monotone; l'analyse du fonctionnement de certains systèmes comme l'outil de coupe dans l'industrie a montré qu'un système peut avoir un mauvais fonctionnement sur une phase et s'améliorer sur la phase suivante. De ce fait, des modifications ont été apportées à la distribution de Weibull afin d'avoir des fonctions de risque de base non monotones, plus particulièrement les fonctions de risque croissantes puis décroissantes. En dépit de ces modifications, la prise en compte des conditions d'opérations extrêmes et la surestimation des risques s'avèrent problématiques. Nous avons donc, à partir de la loi standard de Gumbel, proposé une fonction de risque de base croissante puis décroissante permettant de prendre en compte les conditions extrêmes d'opérations, puis établi les preuves mathématiques y afférant. En outre, un exemple d'application dans le domaine de l'industrie a été proposé. Cette thèse est divisée en quatre chapitres auxquels s'ajoutent une introduction et une conclusion générales. Dans le premier chapitre, nous rappelons quelques notions de base sur la théorie des valeurs extrêmes. Le deuxième chapitre s'intéresse aux concepts de base de l'analyse de survie, particulièrement à ceux relatifs à l'analyse de fiabilité, en proposant une fonction de risque croissante-décroissante dans le modèle à risques proportionnels. En ce qui concerne le troisième chapitre, il porte sur l'utilisation des statistiques d'ordre extrême dans l'usinage, notamment dans la détection de pièces défectueuses par lots, la fiabilité de l'outil de coupe et la modélisation des meilleures surfaces de rugosité. Le dernier chapitre porte sur la prédiction d'éventuelles victimes dans l'Aviation Générale Américaine à partir des données historiques en utilisant l'approche "Peaks-Over Threshold"<br>The operation of a system in general may at any time be affected by an unforeseen incident. When this incident has major consequences on the system integrity and the quality of system products, then it is said to be in the context of extreme events. Thus, increasingly researchers have a particular interest in modeling such events with studies on the reliability of systems and the prediction of the different risks that can hinder the proper functioning of a system. This thesis takes place in this very perspective. We use Extreme Value Theory (EVT) and extreme order statistics as a decision support tool in modeling and risk management in industry and aviation. Specifically, we model the surface roughness of machined parts and the reliability of the associated cutting tool with the extreme order statistics. We also did a modeling using the "Peaks-Over Threshold, POT" approach to make predictions about the potential victims in the American General Aviation (AGA) following extreme accidents. In addition, the modeling of systems subjected to environmental factors or covariates is most often carried out by proportional hazard models based on the hazard function. In proportional hazard models, the baseline risk function is typically Weibull distribution, which is a monotonic function. The analysis of the operation of some systems like the cutting tool in the industry has shown that a system can deteriorated on one phase and improving on the next phase. Hence, some modifications have been made in the Weibull distribution in order to have non-monotonic basic risk functions, more specifically, the increasing-decreasing risk function. Despite these changes, taking into account extreme operating conditions and overestimating risks are problematics. We have therefore proposed from Gumbel's standard distribution, an increasingdecreasing risk function to take into account extreme conditions, and established mathematical proofs. Furthermore, an example of the application in the field of industry was proposed. This thesis is organized in four chapters and to this must be added a general introduction and a general conclusion. In the first chapter, we recall some basic notions about the Extreme Values Theory. The second chapter focuses on the basic concepts of survival analysis, particularly those relating to reliability analysis by proposing a function of increasing-decreasing hazard function in the proportional hazard model. Regarding the third chapter, it deals with the use of extreme order statistics in industry, particularly in the detection of defective parts, the reliability of the cutting tool and the modeling of the best roughness surfaces. The last chapter focuses on the prediction of potential victims in AGA from historical data using the Peaks-Over Threshold approach

Modeling of extreme events is a challenging statistical task. Firstly, there is always a limit number of observations and secondly therefore no experience to back test the result. One way of estimating higher quantiles is to fit one of theoretical distributions to the data and extrapolate to the tail. The shortcoming of this approach is that the estimate of the tail is based on the observations in the center of distribution. Alternative approach to this problem is based on idea to split the data into two sub-populations and model body of the distribution separately from the tail. This methodology is applied to non-life insurance losses, where extremes are particularly important for risk management. Never the less, even this approach is not a conclusive solution of heavy tail modeling. In either case, estimated 99.5% percentiles have such high standard errors, that the their reliability is very low. On the other hand this approach is theoretically valid and deserves to be considered as one of the possible methods of extreme value analysis.

Ce travail de thèse porte sur les outils statistiques pour l'évaluation des maxima de charges de sloshing dans les cuves de méthaniers. Selon les caractéristiques du navire, son chargement et les conditions de navigation, un ballotement hydrodynamique est observé à l'intérieur des cuves, phénomène communément appelé sloshing. La détermination des charges qui s'appliquent à la structure est basée sur des mesures de pression d'impact au moyen d'essais sur maquette. Les maxima de pression par impact, extraits des mesures, sont étudiés. La durée d'un essai est équivalente à 5 heures au réel et insuffisante pour déterminer des maxima de pression associés à de grandes périodes de retour (40 ans). Un modèle probabiliste est nécessaire pour extrapoler les maxima de pression. Le modèle usuel est une loi de Weibull. Comme ce sont les valeurs extrêmes des échantillons qui nous intéressent, les ajustements sont aussi effectués par les lois des valeurs extrêmes et de Pareto généralisées via les méthodes de maximum par bloc et d'excès au-dessus d'un seuil.L'originalité du travail repose sur l'emploi d'un système alternatif, plus pertinent pour la capture des maxima de pression et d'une quantité de 480 heures de mesures disponible pour les mêmes conditions d'essai. Cela fournit une distribution de référence pour les maxima de pression et nous permet d'évaluer la pertinence des modèles sélectionnés. Nous insistons sur l'importance d'évaluer la qualité des ajustements par des tests statistiques et de quantifier les incertitudes sur les estimations obtenues. La méthodologie fournie a été implémentée dans un logiciel nommé Stat_R qui facilite la manipulation et le traitement des résultats<br>This thesis focuses on statistical tools for the assessment of maxima sloshing loads in LNG tanks. According to ship features, tank cargo and sailing conditions, a sloshing phenomenon is observed inside LNG tanks. The determination of sloshing loads supported by the tank structure is derived from impact pressure measurements performed on a test rig. Pressure maxima per impact, extracted from test measurements, are investigated. Test duration is equivalent to 5 hours in full scale. This duration is not sufficient to determine pressure maxima associated with high return periods (40 years). It is necessary to use a probabilistic model in order to extrapolate pressure maxima. Usually, a Weibull model is used. As we focus on extreme values from samples, fittings are also performed with the generalized extreme value distribution and the generalized Pareto distribution using block maximum method and peaks over threshold method.The originality of this work is based on the use of an alternate measurement system which is more relevant than usual measurement system to get pressure maxima and a 480 hours measured data available for same test conditions. This provides a reference distribution for pressure maxima which is used to assess the relevance of the selected probabilistic models. Particular attention is paid to the assessment of fittings quality using statistical tests and to the quantification of uncertainties on estimated values.The provided methodology has been implemented in a software called Stat_R which makes the manipulation and the treatment of results easier

Eventos extremos são raros, mas quando ocorrem têm um enorme impacto social e uma atenção mediática considerável. São exemplo os recordes no mundo do desporto – raros de acontecerem, mas quando ocorrem não apenas são divulgados nos mais variados meios de comunicação social, como são motivo de modificação da metodologia de treino e do comportamento do atleta. Como prever esta ocorrência? Qual a probabilidade de ocorrência? Qual a magnitude da ocorrência? Quanto tempo de espera? A teoria de valores extremos, baseada no teorema dos tipos extremais de Fisher-Tippett- Gnedenko, proporciona um rigoroso quadro de análise dos valores extremos, estimando a probabilidade de ocorrência de eventos que estão para além da amostra disponível. Assim, sob a questão “qual o limite da performance humana?”, este trabalho no domínio da Estatística de Extremos tem aplicações ao desporto de alto rendimento, particularmente às especialidades de lançamentos e saltos do atletismo. Foram utilizadas as metodologias: (i) r-maiores observações, (ii) excessos acima de um limiar, e (iii) máximos de blocos não-estacionários. Decidida a distribuição limite do máximo associado ao evento em estudo e o modelo que melhor se adequa aos dados disponíveis, a estimação pontual dos parâmetros extremais foi realizada por máxima verosimilhança e a estimação intervalar pelo método delta e pela função profile log-likelihood. Em cada método foram testados diversos modelos. Recorremos a técnicas gráficas, estabilidade dos erros-padrão, intervalos de confiança, testes de hipóteses e algumas métricas de erro, para verificação do ajustamento dos modelos aos dados disponíveis. Estamos particularmente interessados na estimação de quantis extremais, probabilidades de excedência, limite superior do suporte, níveis de retorno e período de retorno. Os resultados mostram que nos lançamentos do martelo, disco e dardo feminino existe uma forte probabilidade de se conseguir um novo recorde do mundo e que nos lançamentos masculinos tal probabilidade é reduzida. Com exceção do triplo-salto, nas restantes especialidades de saltos, o período de retorno (i.e., número de máximos individuais) até à ocorrência de um novo recorde do mundo é menor nas mulheres do que nos homens; ABSTRACT: Statistics of Extremes: limits of human performance - study with throwers and jumpers in athletics Extreme events are rare, but when they do occur, they have an enormous social impact and they receive a considerable media attention. Such is the case of world records in sport – they rarely happen, but when they do, not only are they disclosed by all media, but they also cause changes in the training methodology and in the athlete's behaviour. How to predict this occurrence? What is the probability of occurrence? What is the magnitude of the occurrence? How long is the wait? The extreme value theory, based on the Fisher-Tippett-Gnedenko theorem, provides a rigorous framework for analysing extreme values, estimating the probability of the occurrence of events that are beyond the sample. Thus, research within the area of Extreme Statistics provide information to answer the question “what is the limit of human performance?” in the framework of high-performance sport, particularly in the case of the specialties of throwing and jumping in athletics. The methodologies used were: (i) r-largest order statistics, (ii) peaks over threshold, and (iii) non-stationary annual maximum. Once decided the limit distribution of the maximum associated with the event under study and the model that best fits the available data, the point estimation of the extremal parameters were performed by maximum likelihood estimation, with Nelder- Mead or BFGS optimization and the interval estimation using the delta method and the profile loglikelihood function. In each method, several models were tested. We used graphical techniques, stability of standard errors, confidence intervals, hypothesis tests and some error metrics, to verify if the models fit the available data. We were particularly interested in the estimation of extreme quantiles, exceedance probability, right endpoint, return levels and return period. The results suggest that in hammer, discus and javelin throwing there are a strong probability of a new world record will be achieved. In the case of male, throwing events, the forecast of a new world record being achieved with reduced probability. With exception of triple-jump, in all other jumping specialities, the return period (i.e., number of individual maximums) until the occurrence of a new world record is shorter in women than in men.

Title: Modelling dependence between hydrological and meteorological variables measured on several stations Author: Bc. Marie Turčičová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Daniela Jarušková CSc., Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics Abstract: The aim of the thesis is to explore the dependence of daily discharge averages of the Opava river on high daily precipitation values in its basin. Three methods are presented that can be used for analyzing the dependence between high values of random variables. Their application on the studied data is also given. First it is the tail-dependence coefficient that measures the dependence between high values of two continuous random variables. The model for the high quantiles of the discharge at a given precipitation value was first determined non-parametrically by quantile regression and then parametrically through the peaks-over-threshold (POT) method. Keywords: extremal dependence, tail-dependence coefficient, quantile regression, peaks over threshold method

Global warming is affecting the Earth climate year by year, the biggest difference being observable in increasing temperatures in the World Ocean. Following the long- term global ocean warming trend, average sea surface temperatures across the global tropics and subtropics have increased by 0.4–1◦C in the last 40 years. These rates become even higher in semi-enclosed southern seas, such as the Red Sea, threaten- ing the survival of thermal-sensitive species. As average sea surface temperatures are projected to continue to rise, careful study of future developments of extreme temper- atures is paramount for the sustainability of marine ecosystem and biodiversity. In this thesis, we use Extreme-Value Theory to study sea surface temperature extremes from a gridded dataset comprising 16703 locations over the Red Sea. The data were provided by Operational SST and Sea Ice Analysis (OSTIA), a satellite-based data system designed for numerical weather prediction. After pre-processing the data to account for seasonality and global trends, we analyze the marginal distribution of ex- tremes, defined as observations exceeding a high spatially varying threshold, using the Generalized Pareto distribution. This model allows us to extrapolate beyond the ob- served data to compute the 100-year return levels over the entire Red Sea, confirming the increasing trend of extreme temperatures. To understand the dynamics govern- ing the dependence of extreme temperatures in the Red Sea, we propose a flexible local approach based on R-Pareto processes, which extend the univariate Generalized Pareto distribution to the spatial setting. Assuming that the sea surface temperature varies smoothly over space, we perform inference based on the gradient score method over small regional neighborhoods, in which the data are assumed to be stationary in space. This approach allows us to capture spatial non-stationarity, and to reduce the overall computational cost by taking advantage of distributed computing resources. Our results reveal an interesting extremal spatial dependence structure: in particular, from our estimated model, we conclude that significant extremal dependence prevails for distances up to about 2500 km, which roughly corresponds to the Red Sea length.