The thesis has for objective to study new statistical methods to correct temperature predictionsthat may be implemented on the ensemble prediction system (EPS) of Meteo France so toimprove its use for the electric system management, at EDF France. The EPS of Meteo Francewe are working on contains 51 members (forecasts by time-step) and gives the temperaturepredictions for 14 days. The thesis contains three parts: in the first one we present the EPSand we implement two statistical methods improving the accuracy or the spread of the EPS andwe introduce criteria for comparing results. In the second part we introduce the extreme valuetheory and the mixture models we use to combine the model we build in the first part withmodels for fitting the distributions tails. In the third part we introduce the quantile regressionas another way of studying the tails of the distribution.

Market Timing Strategy is an active investment strategy, which is based on the signals of indicators, for the investors to make their investment decisions. However, there has always been the question on which variable is a good indicator, that would provide superior returns for the investment. Bond to Equity Yield Ratio (BEYR) is a new indicator widely researched by many academics in the field of finance and extensively applied by practitioners of the financial markets during the last two decades. Efficient Market Hypothesis (EMH) is a theory in finance which states that stock prices are always reflected with the relevant information and beating the market from predicting the trend of future stock prices is not possible. Therefore, if the market is in accordance with EMH, market timing strategy is not useful and passive investment strategy is better than active investment strategy. Although extant literatures have proved BEYR as a good indicator to be used in market timing strategy, the focus of the existing research is on the financial markets in the United States, the United Kingdom, and the Europe; the study on Asian financial markets is very limited. The main objective of the research is mainly motivated by this knowledge gap. This study will use extreme value strategy as an active trading strategy to conduct research on the market timing ability of BEYR in three Asian financial markets: Japan, Malaysia and Singapore. In addition, passive trading strategy will be used to compare with active trading strategy in each country to identify whether the markets comply with weak form of EMH. Deductive approach of quantitative research is conducted and three main hypotheses are developed to achieve the research objective. The empirical findings from our research and the responses to the main hypotheses can be summarized as active trading strategy does perform better than passive trading strategy for all countries and the market timing ability of BEYR is not as good as the traditional indicators: dividend yields and earning yields for all countries. Therefore, the financial markets of all counties under scrutiny do not comply with weak form of EMH. However, it is worthy to take note that the sample period chosen for this research includes the period when the Global Financial Crisis occurred in 2008. Therefore, it is assumed that the impact of the financial crisis is the main reason contributing the difference between the findings from our research and the existing literatures. Moreover, the difference in the nature of financial market can be considered as another underlying factor for the new perspective on BEYR resulting from our empirical results.

The heavy-tailed traffic from wireless users, caused by the emerging Internet and multimedia applications, induces extremely dynamic and variable network environment, which can fundamentally change the way in which wireless networks are conceived, designed, and operated. This thesis is concerned with modeling, analysis, and optimization of wireless networks in the presence of heavy tails. First, a novel traffic model is proposed, which captures the inherent relationship between the traffic dynamics and the joint effects of the mobility variability of network users and the spatial correlation in their observed physical phenomenon. Next, the asymptotic delay distribution of wireless users is analyzed under different traffic patterns and spectrum conditions, which reveals the critical conditions under which wireless users can experience heavy-tailed delay with significantly degraded QoS performance. Based on the delay analysis, the fundamental impact of heavy-tailed environment on network stability is studied. Specifically, a new network stability criterion, namely moment stability, is introduced to better characterize the QoS performance in the heavy-tailed environment. Accordingly, a throughput-optimal scheduling algorithm is proposed to maximize network throughput while guaranteeing moment stability. Furthermore, the impact of heavy-tailed spectrum on network connectivity is investigated. Towards this, the necessary conditions on the existence of delay-bounded connectivity are derived. To enhance network connectivity, the mobility-assisted data forwarding scheme is exploited, whose important design parameters, such as critical mobility radius, are derived. Moreover, the latency in wireless mobile networks is analyzed, which exhibits asymptotic linearity in the initial distance between mobile users.

The research presented in this dissertation attempted to determine whether climate variability is critical to sea level changes in coastal BC. To that end, a number of statistical models were proposed to clarify the relationships between five climate variability indices representing large-scale atmospheric circulation regimes and sea levels, storm surges, extreme winds and storm track variability in coastal BC. The research findings demonstrate that decadal to inter decadal climatic variability is fundamental to explaining the changing frequency and intensity of extreme atmospheric and oceanic environmental variables in coastal BC. The trends revealed by these analyses suggest that coastal flooding risks are certain to increase in this region during the next few decades, especially if the global sea-levels continue to rise as predicted. The out come of this study emphasis the need to look beyond climatic means when completing climate impact assessments, by clearly showing that climate extremes are currently causing the majority of weather-related damage along coastal BC. The findings highlight the need to derive knowledge on climate variability and change effects relevant at regional to local scales to enable useful adaptation strategies. The major findings of this research resulted in five independent manuscripts: (i) Sea level responses to climatic variability and change in Northern BC. The Manuscript (MC) is published in the Journal of atmospheric and oceans (AO 46 (3), 277-296); (ii) Extreme sea-level recurrences in the south coast of BC with climate considerations. This MC is in review with the Asia Pacific Journal of Climate Change (APJCC); (iii) Extreme sea-surge responses to climate variability in coastal BC. This MC is currently in review in the Annals of the AAG (AN-2009-0098); (iv) Extreme wind regime responses to climate variability and change in the inner-south-coast of BC. This MC is published in the Journal of Atmosphere and Oceans (AO 47 (1), 41-62); (v) Sensitivity of winter storm track characteristics in North-eastern Pacific to climate variability. This manuscript is in review with the Journal of Atmosphere and Oceans (AO (1113)). The findings of this research program made key contributions to the following regional sea level rise impact assessment studies in BC: (i) An examination of the Factors Affecting Relative and Absolute Sea level in coastal BC (Thomson et al., 2008). (ii) Coastal vulnerability to climate change and sea level rise, Northeast Graham Island, Haida Gwaii (formally known as the Queen Charlotte Islands), BC (Walker et al., 2007). (iii) Storm Surge: Atmospheric Hazards, Canadian Atmospheric Hazards Network - Pacific and Yukon Region, C/O Bill Taylor.

Intensity-Duration-Frequency (IDF) curves are among the standard design tools for various engineering applications, such as storm water management systems. The current practice is to use IDF curves based on historical extreme precipitation quantiles. A warming climate, however, might change the extreme precipitation quantiles represented by the IDF curves, emphasizing the need for updating the IDF curves used for the design of urban storm water management systems in different parts of the world, including Canada. This study attempts to construct the future IDF curves for Saskatoon, Canada, under possible climate change scenarios. For this purpose, LARS-WG, a stochastic weather generator, is used to spatially downscale the daily precipitation projected by Global Climate Models (GCMs) from coarse grid resolution to the local point scale. The stochastically downscaled daily precipitation realizations were further disaggregated into ensemble hourly and sub-hourly (as fine as 5-minute) precipitation series, using a disaggregation scheme developed using the K-nearest neighbor (K-NN) technique. This two-stage modeling framework (downscaling to daily, then disaggregating to finer resolutions) is applied to construct the future IDF curves in the city of Saskatoon. The sensitivity of the K-NN disaggregation model to the number of nearest neighbors (i.e. window size) is evaluated during the baseline period (1961-1990). The optimal window size is assigned based on the performance in reproducing the historical IDF curves by the K-NN disaggregation models. Two optimal window sizes are selected for the K-NN hourly and sub-hourly disaggregation models that would be appropriate for the hydrological system of Saskatoon. By using the simulated hourly and sub-hourly precipitation series and the Generalized Extreme Value (GEV) distribution, future changes in the IDF curves and associated uncertainties are quantified using a large ensemble of projections obtained for the Canadian and British GCMs (CanESM2 and HadGEM2-ES) based on three Representative Concentration Pathways; RCP2.6, RCP4.5, and RCP8.5 available from CMIP5 – the most recent product of the Intergovernmental Panel on Climate Change (IPCC). The constructed IDF curves are then compared with the ones constructed using another method based on a genetic programming technique. The results show that the sign and the magnitude of future variations in extreme precipitation quantiles are sensitive to the selection of GCMs and/or RCPs, and the variations seem to become intensified towards the end of the 21st century. Generally, the relative change in precipitation intensities with respect to the historical intensities for CMIP5 climate models (e.g., CanESM2: RCP4.5) is less than those for CMIP3 climate models (e.g., CGCM3.1: B1), which may be due to the inclusion of climate policies (i.e., adaptation and mitigation) in CMIP5 climate models. The two-stage downscaling-disaggregation method enables quantification of uncertainty due to natural internal variability of precipitation, various GCMs and RCPs, and downscaling methods. In general, uncertainty in the projections of future extreme precipitation quantiles increases for short durations and for long return periods. The two-stage method adopted in this study and the GP method reconstruct the historical IDF curves quite successfully during the baseline period (1961-1990); this suggests that these methods can be applied to efficiently construct IDF curves at the local scale under future climate scenarios. The most notable precipitation intensification in Saskatoon is projected to occur with shorter storm duration, up to one hour, and longer return periods of more than 25 years.

This thesis presents a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphical models for probability density and mass functions, in a CDN, the marginal probabilities for any subset of variables are obtained by computing limits of functions in the model. We will show that the conditional independence properties in a CDN are distinct from the conditional independence properties of directed, undirected and factor graph models, but include the conditional independence properties of bidirected graphical models. As a result, CDNs are a parameterization for bidirected models that allows us to represent complex statistical dependence relationships between observable variables. We will provide a method for constructing a factor graph model with additional latent variables for which graph separation of variables in the corresponding CDN implies conditional independence of the separated variables in both the CDN and in the factor graph with the latent variables marginalized out. This will then allow us to construct multivariate extreme value distributions for which both a CDN and a corresponding factor graph representation exist. In order to perform inference in such graphs, we describe the `derivative-sum-product' (DSP) message-passing algorithm where messages correspond to derivatives of the joint cumulative distribution function. We will then apply CDNs to the problem of learning to rank, or estimating parametric models for ranking, where CDNs provide a natural means with which to model multivariate probabilities over ordinal variables such as pairwise preferences. We will show that many previous probability models for rank data, such as the Bradley-Terry and Plackett-Luce models, can be viewed as particular types of CDN. Applications of CDNs will be described for the problems of ranking players in multiplayer team-based games, document retrieval and discovering regulatory sequences in computational biology using the above methods for inference and estimation of CDNs.

一般而言財務資料具有高峰(High Kurtosis)及厚尾(Heavy Tail)的特性，極值理論(Extreme Value Theorem)即是著重於尾部極端事件發生的機率，描繒出尾部極端值的機率分配，以捕捉財務資料中具厚尾的現象，利用估算尾部指數(Tail Index) α值判斷尾部分配的厚、薄程度。一般在估算α值時均是假設α值是不會隨著時間而變動的穩定值，然而在我們所選取的樣本期間內，可能伴隨著一些重大事件，如金融風暴、或是制度面的改變等，均有可能造成尾部極端值發生機率的增加或減少，因此在其樣本期間所估算的α值不應假設為一不變的常數。本文即是針對亞洲四小龍的匯率資料做”尾部參數是否發生結構變化(Structural Change)”之假設檢定，並且找出發生結構變化的時點。 實証結果發現，在1993~2004年間，亞洲四小龍的匯率報酬率其尾部參數確實有發生結構變化的情形。此結論對於風險管理者而言，必須注意到尾部參數α值應該是一個會隨著時間而改變的值，也就是在估算 值時應該要避開發生結構變化的可能時點，或許應於所要估計的樣本期間先執行尾部參數是否有結構變化的檢定，如此才能更準確的估算α值。

Portfolio Management is the process of allocating an investor's wealth to in­ vestment opportunities over a given planning period. Not only should Portfolio Management be treated within a multi-period framework, but one should also take into consideration the stochastic nature of related parameters. After a short review of key concepts from Finance Theory, e.g. utility function, risk attitude, Value-at-rusk estimation methods, a.nd mean-variance efficiency, this work describes a framework for the formulation of the Portfolio Management problem in a Stochastic Programming setting. Classical solution techniques for the resolution of the resulting Stochastic Programs (e.g. L-shaped Decompo­ sition, Approximation of the probability function) are presented. These are discussed within both the two-stage and the multi-stage case with a special em­ phasis on the former. A description of how Importance Sampling and EVPI are used to improve the efficiency of classical methods is presented. Postoptimality Analysis, a sensitivity analysis method, is also described. / Statistics / M. Sc. (Operations Research)

[pt] Nesta dissertação avalia-se o grau de associação entre pares de excessos de retornos, simultâneos e defasados no tempo, usando-se o conceito de cópulas. Cópulas assimétricas são ajustadas aos pares de distribuições de retornos e coeficientes de dependência de cauda, as medidas de interdependência e contágio baseadas nessas cópulas, são calculados para 10 pares de índices de mercados. Tais coeficientes balizam a escolha do par de ativos com melhor desempenho em períodos de estresse. Se excessos defasados são incluídos, então estes coeficientes também indicam a direção e intensidade de propagação das crises (contágio). Os resultados encontrados na nossa investigação mostram que a técnica utilizada é eficaz na montagem de carteiras em que se pretende aproveitar os ganhos extremos conjuntos dos ativos e, ao mesmo tempo, evitar perdas extremas conjuntas. O uso de retornos defasados, porém, foi um artifício pouco producente, refletindo possivelmente o contágio quase instantâneo entre os mercados financeiros mundiais, nos dias de hoje. / [en] In this dissertation we evaluate the degree of association between pairs of excess of returns, simultaneous and lagged, using the concept of copulas. Asymmetric copulas are fitted to 10 pairs of distributions of returns of world markets índices. From these copulas coefficients of tail dependence are obtained for the right and left tails. Isong those coefficients as measures of cross dependence and contagion between markets one can pick the pair of returns that show the best performance in periods of stress. If lagged excess of returns are included, then these coefficients provide information on the direction and intensity of the contagion spread. Our results have shown that such technique isd efficent in constructing a portfolio in which one wants to take advantage of joint extreme gains of pairs of returns and, simultaneously, avoid losses associated with the occurrence of joint negative extremes. The use of lagged returns in this context hás shown no extra gain, maybe reflecting the fact that, nowadays, the spread of contagion between world financial markets is almost instantaneous.

Made available in DSpace on 2016-12-23T14:00:36Z (GMT). No. of bitstreams: 1 Danilo Soares Monte-Mor.pdf: 964390 bytes, checksum: 749870f88ee1c9c692cf782e397379ec (MD5) Previous issue date: 2010-12-17 / Cada vez mais tem surgido no mercado de investimento fundos de retorno absoluto (Hedge Funds) que têm como objetivo principal melhorar seus desempenhos através de estratégias de arbitragem, como é o caso das estratégias long-short. É o comportamento desproporcional e até mesmo antagônico dos preços dos ativos que permite aos players estruturar estratégias para gerar retornos adicionais, superiores aos custos de oportunidade e independentes ao movimento do mercado. Neste trabalho foi utilizada a Teoria de Valores Extremos (TVE), um importante ramo da probabilidade, para que fossem modeladas as séries da relação direta entre preços de dois pares de ativos. Os quantis obtidos a partir de tal modelagem, juntamente com os quantis fornecidos pela normal, foram superpostos aos dados para períodos subsequentes ao período analisado. A partir da comparação desses dados foi criada uma nova estratégia quantitativa long-short de arbitragem, a qual denominamos GEV Long-Short Strategy / Increasingly has appeared on the market of investment Absolute Return Funds (Hedge Funds), which have the main objective to improve their performance through arbitrage strategies, as long-short strategies. It is the disproportionate evolution and even antagonistic of active prices that allows the players to structure strategies to generate additional returns, higher than the opportunity costs and independent of the movement of the market. In this work we used Extreme Value Theory (EVT), an important segment of probability, to model the series of direct relationship between prices of two pairs of assets. The quantiles obtained from such modeling and the quantile provided by normal were superimposed on data for periods subsequent to the period analyzed. From the comparison of such data we created a new quantitative long-short arbitrage strategy, called GEV Long-Short Strategy