Em testes nos quais uma quantidade considerável de indivíduos não dispõe de tempo suciente para responder todos os itens temos o que é chamado de efeito de Speededness. O uso do modelo unidimensional da Teoria da Resposta ao Item (TRI) em testes com speededness pode nos levar a uma série de interpretações errôneas uma vez que nesse modelo é suposto que os respondentes possuem tempo suciente para responder todos os itens. Nesse trabalho, desenvolvemos uma análise Bayesiana do modelo tri-dimensional da TRI proposto por Wollack e Cohen (2005) considerando uma estrutura de dependência entre as distribuições a priori dos traços latentes a qual modelamos com o uso de cópulas. Apresentamos um processo de estimação para o modelo proposto e fazemos um estudo de simulação comparativo com a análise realizada por Bazan et al. (2010) na qual foi utilizada distribuições a priori independentes para os traços latentes. Finalmente, fazemos uma análise de sensibilidade do modelo em estudo e apresentamos uma aplicação levando em conta um conjunto de dados reais proveniente de um subteste do EGRA, chamado de Nonsense Words, realizado no Peru em 2007. Nesse subteste os alunos são avaliados por via oral efetuando a leitura, sequencialmente, de 50 palavras sem sentidos em 60 segundos o que caracteriza a presença do efeito speededness. / In tests where a reasonable amount of individuals does not have enough time to answer all items we observe what is called eect of Speededness. The use of a unidimensional model from Item Response Theory (IRT) in tests with speededness can lead us to erroneous interpretations, since this model assumes that the respondents have enough time to answer all items. In this work, we propose a Bayesian analysis of the three-dimensional item response models (IRT) proposed by Wollack and Cohen et al (2005) considering a dependency structure between the prior distributions of the latent traits which is modeled using Copulas. We propose and develop a MCMC algorithm for the estimation of the model. A simulation study comparing with the analysis in Bazan et al (2010), wherein an independent prior distribution assumption was presented. Finally, we apply our model in a set of real data from EGRA, called Nonsense Words, held in Peru in 2007, where students are evaluated for their performance in reading.

As diversas crises financeiras e econômicas ocorridas nas últimas décadas geraram uma demanda pelo estudo da propagação destes efeitos entre as economias. Neste sentido este trabalho tem como objetivo estudar o efeito contágio (Shift Contagion) tal como definido em Rigobon (2002) do mercado financeiro do Brasil para quatro países para o período de 2011 a 2016, que inclui a recente crise econômica no Brasil. Tais países são Argentina, Colômbia, Chile, e Peru. Para tal, utilizou-se metodologia de cópulas paramétricas estáticas. Com base nos resultados obtidos, não é possível identificar indícios da ocorrência de contágio do mercado financeiro brasileiro para os mercados financeiros dos países analisados no período do estudo. / Different financial and economic crises that occurred in the last decades have generated a demand of studies on propagation of their effects between economies. In this sense, this work has the goal to study the contagion effect (shift contagion), as defined by Rigobon (2002), from the Brazilian financial market to four countries in the period from 2011 to 2016 that includes the recent Brazilian economic crisis. These countries are Argentina, Colombia, Chile, and Peru. For this purpose, the methodology of parametric static copulas is used. Accordingly with the results, it is not possible to identify evidences of the contagion effect from the Brazilian financial market to the analyzed countries.

In this dissertation we solve the nonidentifiability problem of Archimedean copula models based on dependent censored data (see [Wang, 2012]). We give a set of identifiability conditions for a special class of bivariate frailty models. Our simulation results show that our proposed model is identifiable under our proposed conditions. We use EM algorithm to estimate unknown parameters and the proposed estimation approach can be applied to fit dependent censored data when the dependence is of research interest. The marginal survival functions can be estimated using the copula-graphic estimator (see [Zheng and Klein, 1995] and [Rivest and Wells, 2001]) or the estimator proposed by [Wang, 2014]. We also propose two model selection procedures for Archimedean copula models, one for uncensored data and the other one for right censored bivariate data. Our simulation results are similar to that of [Wang and Wells, 2000] and suggest that both procedures work quite well. The idea of our proposed model selection procedure originates from the model selection procedure for Archimedean copula models proposed by [Wang and Wells, 2000] for right censored bivariate data using the L2 norm corresponding to the Kendall distribution function. A suitable bootstrap procedure is yet to be suggested for our method. We further propose a new parameter estimator and a simple goodness-of-fit test for Archimedean copula models when the bivariate data is under fixed left truncation. Our simulation results suggest that our procedure needs to be improved so that it can be more powerful, reliable and efficient. In our strategy, to obtain estimates for the unknown parameters, we heavily exploit the concept of truncated tau (a measure of association established by [Manatunga and Oakes, 1996] for left truncated data). The idea of our goodness of fit test originates from the goodness-of-fit test for Archimedean copula models proposed by [Wang, 2010] for right censored bivariate data.

Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. The analysis of dependence via copula models has been focussed on the bivariate case mainly. In the vast majority of instances symmetric elliptical copulas are employed to model dependence for severities. This thesis proposes a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severities, and to calculate the capital for operational risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mixture distribution (the Lognormal for the body of losses and the generalised Pareto Distribution for the tail) using a technique from extreme value theory, (ii) the multivariate skew t-copula applied for the first time across severities and (iii) Bayesian theory. The former to model severities, I test simultaneously several parametric distributions and the mixture distribution for each business line. This procedure enables me to achieve multiple combinations of the severity distribution and to find which fits most closely. The second to effectively model asymmetry and extreme dependence in high dimensions. The third to estimate the copula model, given the high multivariate component (i.e. eight business lines and seven event types) and the incorporation of mixture distributions it is highly difficult to implement maximum likelihood. Therefore, I use a Bayesian inference framework and Markov chain Monte Carlo simulation to evaluate the posterior distribution to estimate and make inferences of the parameters of the skew t-copula model. The research analyses an updated operational loss data set, SAS® Operational Risk Global Data (SAS OpRisk Global Data), to model operational risk at international financial institutions. I then evaluate the impact of this multivariate, asymmetric and extreme dependence on estimating the total regulatory capital, among other established multivariate copulas. My empirical findings are consistent with other studies reporting thin and medium-tailed loss distributions. My approach substantially outperforms symmetric elliptical copulas, demonstrating that modelling dependence via the skew t-copula provides a more efficient allocation of capital charges of up to 56% smaller than that indicated by the standard Basel model.

A modelagem da estrutura de dependência é de grande importância em todos os ramos da economia onde há incerteza. Ela é um elemento crucial na análise de risco e para a tomada de decisão sob incerteza. As cópulas oferecem aos agentes que se deparam com este problema um poderoso e flexível instrumento para modelar a estrutura de dependência entre variáveis aleatórias e que é preferível ao instrumento tradicional baseado na correlação linear. Neste estudo, nós analisamos a dinâmica temporal da estrutura de dependência entre índices de mercados financeiros internacionais e propomos um novo procedimento para capturar a estrutura de dependência ao longo do tempo. Adicionalmente, estudamos alguns fatos estilizados sobre índices de mercados financeiros como a relação entre volume-volatilidade e retorno-volatilidade. / Modelling dependence is of key importance to all economic fields in which uncertainty plays a large role. It is a crucial element of risk analysis and decision making under uncertainty. Copulas offer economic agents facing uncertainty a powerful and flexible tool to model dependence between random variables and often are preferable to the traditional, correlation-based approach. In this work we analyze the time dynamics of the dependence structure between broad stock market indices and propose a novel procedure to capture dependence structure over time. Additionally, we study some stylized facts about stock market indexes such as volume-volatility and return-volatility relations.

Em testes nos quais uma quantidade considerável de indivíduos não dispõe de tempo suciente para responder todos os itens temos o que é chamado de efeito de Speededness. O uso do modelo unidimensional da Teoria da Resposta ao Item (TRI) em testes com speededness pode nos levar a uma série de interpretações errôneas uma vez que nesse modelo é suposto que os respondentes possuem tempo suciente para responder todos os itens. Nesse trabalho, desenvolvemos uma análise Bayesiana do modelo tri-dimensional da TRI proposto por Wollack e Cohen (2005) considerando uma estrutura de dependência entre as distribuições a priori dos traços latentes a qual modelamos com o uso de cópulas. Apresentamos um processo de estimação para o modelo proposto e fazemos um estudo de simulação comparativo com a análise realizada por Bazan et al. (2010) na qual foi utilizada distribuições a priori independentes para os traços latentes. Finalmente, fazemos uma análise de sensibilidade do modelo em estudo e apresentamos uma aplicação levando em conta um conjunto de dados reais proveniente de um subteste do EGRA, chamado de Nonsense Words, realizado no Peru em 2007. Nesse subteste os alunos são avaliados por via oral efetuando a leitura, sequencialmente, de 50 palavras sem sentidos em 60 segundos o que caracteriza a presença do efeito speededness. / In tests where a reasonable amount of individuals does not have enough time to answer all items we observe what is called eect of Speededness. The use of a unidimensional model from Item Response Theory (IRT) in tests with speededness can lead us to erroneous interpretations, since this model assumes that the respondents have enough time to answer all items. In this work, we propose a Bayesian analysis of the three-dimensional item response models (IRT) proposed by Wollack and Cohen et al (2005) considering a dependency structure between the prior distributions of the latent traits which is modeled using Copulas. We propose and develop a MCMC algorithm for the estimation of the model. A simulation study comparing with the analysis in Bazan et al (2010), wherein an independent prior distribution assumption was presented. Finally, we apply our model in a set of real data from EGRA, called Nonsense Words, held in Peru in 2007, where students are evaluated for their performance in reading.

Cette thèse examine l’alternance en romani du Mexique de la copule si et des clitiques sujet -lo ; -li/-la ; -le. Il s’agit d’un phénomène linguistique absent de toutes les variétés romani parlées en Europe et qui selon Adamou (2013) s’est développé sous l’influence de l’espagnol dans les communautés romani installées en Amérique Latine depuis le 19e siècle. La présente étude s’appuie des données originales collectées auprès de locuteurs bilingues de la communauté de La Rinconada dans l’État de Veracruz au Mexique. En analysant un corpus oral spontané d’environ 16 heures et les réponses de 60 personnes à un questionnaire de choix de copule, j’ai pu dégager les variables qui sous-tendent l’emploi des copules en espagnol et romani. Les variables linguistiques décrites traditionnellement pour la variation des copules ser et estar en espagnol, comme par exemple le Cadre de référence et le Type de prédicat, s’avèrent aussi pertinentes pour comprendre l’emploi des copules romani. Les clitiques sujet romani sont particulièrement dynamiques dans les constructions de troisième personne affirmatives au présent où ils tendent à éclipser la copule romani traditionnelle si. Il est possible d’argumenter que cette expansion provoquée par le contact avec l’espagnol influence à son tour l’emploi des copules en espagnol. En effet, on observe parallèlement un dynamisme de la copule estar et son extension à des contextes précédemment occupés par la copule ser, une tendance plus générale documentée par ailleurs pour l’espagnol du Mexique. / This thesis examines the alternation in of the Romani copula si and the subject clitics lo; -li/-la; -le. It is a linguistic phenomenon that is absent from all the Romani varieties spoken in Europe and which according to Adamou (2013) has been developed under the influence of Spanish in the Romani communities who have settled in Latin America since the 19th century. This study has been possible thanks to the collection of original data from bilingual speakers of the community of La Rinconada in the State of Veracruz in Mexico. Based on the analysis of a spontaneous oral corpus of approximately 16 hours and responses from 60 participants to a questionnaire of copula choice, I was able to identify the variables underlying the use of copulas in both languages. The linguistic variables described for the variation of the copulas ser and estar in Spanish, as for example the frame of reference and the type of predicate, are also relevant to understand the use of copulas in Romani. However, it appears clearly that the Romani subject clitics are particularly dynamic in present affirmative constructions of third person where they tend to overshadow the traditional Romani copula si. It is possible to argue that this expansion that started under the influence of Spanish is now in turn influencing the use of Spanish copulas. Indeed, there is in parallel a dynamic use of the copula estar and extension to contexts previously covered by the copula ser, following a more general trend documented in Mexican Spanish.

The increase in the use of copulas has introduced implementation issues for both practitioners and researchers. One of the issues is to obtain a copula function for a given set of data. The most common approaches for the estimation of the parameters of the copula functions have been the Maximum Likelihood Estimator (MLE) and the Inference Functions for Margins (IFM) methods. Archimedean copulas are one of the most important classes of copulas that are widely used in both finance and insurance for modelling dependent risks. However, simulating multivariate Archimedean copulas has always been a difficult task as the number of dimensions increases. The assessment of capital requirements has always been an important application of stochastic modelling. Capital requirements can vary significantly depending on the model adopted. Several professional bodies have recently discussed the concept of dependencies between insurance risks. They suggest that insurers should use a technique based on copulas to describe the dependence of risks within an insurance company in the context of solvency assessment. The first contribution of this thesis is to provide an insight into the efficiency of parameter estimation methods. This thesis uses numerical experiments to assess the performance of the two common approaches. The second contribution of this thesis is to present a new algorithm to simulate multivariate Exchangeable Archimedean copulas. This algorithm provides a practical solution for simulating one-parameter multivariate Archimedean copulas. Numerical experiments are used to apply this algorithm to determine the "additional" economic capital for an insurance company with multiple lines of business that wants to expand its business by adding another line of business and where the businesses are dependent. The third contribution of this thesis is to quantify the impact of the choice of copulas on the solvency measure of a general insurer within a Dynamic Financial Analysis modelling framework. The results of our experiments provide important guidance for the capital assessment for general insurers.

This thesis contributes to the econometric literature in two ways. Firstly, it introduces a new multivariate count model that presents advances in several aspects. Our multivariate time series count model can deal with issues of discreteness, overdispersion (variance greater than the mean) and both cross- and serial correlation, all at the same time. We follow a fully parametric approach and specify a marginal distribution for the counts where, conditionally on past observations the means follow a vector autoregressive process (VAR). This enables to attain improved inference on coefficients of exogenous regressors relative to the static Poisson regression, while modelling the serial correlation in a flexible way. The method is also innovative in the use of copulas, which builds the dependence structure between variables with given marginal distributions. This makes it possible to model the contemporaneous correlation between individual series in a very flexible way. Secondly, this thesis introduces a new approach to estimate the multivariate reduced rank regressions when the normality assumption is not satisfied. We propose to use the copula tool to generate multivariate distributions and, we show that this method can be applied in multivariate settings. In terms of financial literature, this thesis provides two contributions. Firstly, with our multivariate count model we analyze diverse market microstructure issues about the submission of different types of orders by traders on stock markets. With this model, we can fully take into account the interactions between submissions of the various types of orders, which represent an advantage with respect to univariate models such as the autoregressive conditional duration model. Secondly, it contributes to portfolio research proposing a new dynamic optimal portfolio allocation model in a Value-at-Risk setup. This model allows for time varying skewness and kurtosis of portfolio distributions and the model parameters are estimated by weighted maximum likelihood in an increasing window setup. This last property allows us to have more accurate portfolio recommendations in terms of the amount to invest in the risk-free interest rate and in the risky portfolio.

This thesis develops models and associated Bayesian inference methods for flexible univariate and multivariate conditional density estimation. The models are flexible in the sense that they can capture widely differing shapes of the data. The estimation methods are specifically designed to achieve flexibility while still avoiding overfitting. The models are flexible both for a given covariate value, but also across covariate space. A key contribution of this thesis is that it provides general approaches of density estimation with highly efficient Markov chain Monte Carlo methods. The methods are illustrated on several challenging non-linear and non-normal datasets. In the first paper, a general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student-t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. The second paper explores how well a smooth mixture of symmetric components can capture skewed data. Simulations and applications on real data show that including covariate-dependent skewness in the components can lead to substantially improved performance on skewed data, often using a much smaller number of components. We also introduce smooth mixtures of gamma and log-normal components to model positively-valued response variables. In the third paper we propose a multivariate Gaussian surface regression model that combines both additive splines and interactive splines, and a highly efficient MCMC algorithm that updates all the multi-dimensional knot locations jointly. We use shrinkage priors to avoid overfitting with different estimated shrinkage factors for the additive and surface part of the model, and also different shrinkage parameters for the different response variables. In the last paper we present a general Bayesian approach for directly modeling dependencies between variables as function of explanatory variables in a flexible copula context. In particular, the Joe-Clayton copula is extended to have covariate-dependent tail dependence and correlations. Posterior inference is carried out using a novel and efficient simulation method. The appendix of the thesis documents the computational implementation details. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: In press. Paper 4: Manuscript.</p>