This thesis studies mean-field games (MFGs) models of price formation. The thesis focuses explicitly on a MFGs price formation model proposed by Gomes and Saude. The thesis is divided into two parts. The first part examines the deterministic supply case, while the second part extends the model to incorporate a stochastic supply function. We explore different approaches, such as Aubry-Mather theory, to study the properties of the MFGs price formation model and alternative formulations using a convex variational problem with constraints. We propose machine-learning-based numerical methods to approximate the solution of the MFGs price formation model in the deterministic and stochastic setting.

[pt] Essa tese considera um modelo não linear para se obter previsões de curto prazo de carga de energia elétrica. O modelo combina um modelo de múltiplos regimes auto-regressivo com transição suave com um periódico auto-regressivo criando o modelo de múltiplos regimes periódico com transição suave (STPAR). Um método de construção do modelo é desenvolvido com métodos estatísticos simples e um teste de linearidade contra a hipótese de modelo periódico autoregressivo com transição suave. Outros dois destes foram elaborados para se avaliar o modelo estimado: um teste de Multiplicador de Lagrange (LM) para a hipótese de auto-correlação serial dos resíduos e outro teste LM para a hipótese de não linearidade remanescente. Um experimento de Monte Carlo foi implementado para avaliar a performance dos testes propostos. Estimação por mínimos quadrados não lineares é considerado. Finalmente, dados de carga de energia elétrica do estado de New South Wales na Austrália são apresentados e foram usados como exemplo real. Outros modelos foram utilizados para comparar a performance do modelo. / [en] This thesis considers a non linear approach to obtain short term forecast for electricity load. The model combines a smooth transition autoregressive process with a periodic autoregressive time series model, creating the Smooth Transition Periodic Autoregressive (STPAR) model. A model-building procedure is developed and a linearity test against smooth transition periodic auto-regressive is proposed. Other two tests were created to evaluate the model: a Lagrange multiplier (LM) test for the hypothesis of no error autocorrelation and LM-type test for the hypothesis of no remaining non-linearity. A Monte Carlo experiment was implemented to evaluate the performance of the proposed tests. Estimation by nonlinear least squares is considered. Finally, load data from New South Wales State in Australia`s electricity retail market is presented and will be used as a real example. Other models were used to compare the performance of the proposes model.

[pt] Neste trabalho apresenta-se uma metodologia pelo método dos elementos finitos para a análise estática-dinâmica bi-dimensional de linhas marítimas considerando-se o contato com o leito marinho. Para o cabo considera-se o elemento de dois nós do modelo de viga de Euler-Bernoulli com as grandezas estáticas e dinâmicas referidas a um sistema co- rotacionado. Considera-se a nãolinearidade geométrica associada ao movimento de corpo rígido da estrutura, supondo pequenas deformações. No movimento da linha, são consideradas as influências do peso próprio, empuxo, carregamentos hidrodinâmicos das correntes marinhas, deslocamentos prescritos no ponto superior da linha, forças de inercia e ação de flutuadores. Os efeitos sobre a linha associados ao contato com o fundo marinho são considerados empregando-se a técnica dos multiplicadores de Lagrange. Estes representam o carregamento (forças e momentos) requerido para garantir as restrições geométricas. No modelo não são considerados os efeitos das forças de atrito com o fundo marinho, cuja rigidez é considerada muito superior à do cabo. A matriz de rigidez usual do modelo de vigas é aumentada de forma a acomodar as novas incógnitas resultantes da imposição das condições de contato. Desta forma, condições de contato, separação repetidos (contato variável) e grandes movimentos relativos do cabo com o leito são contemplados pelo modelo. A solução das equações algébricas não-lineares, resultantes da integração temporal passo-a-passo de Newmark, é obtida com a técnica iterativa de Newton Raphson. A metodologia numérica foi implementada e resultados de alguns testes para situações da engenharia offshore são mostrados e comparados com os apresentados por outros autores independentes. / [en] In this work a finite element methodology for two- dimensional static and/or dynamic analysis of maritime risers including contact with the seabed is considered. The line is modeled by a two node beam element based on the Euler- Bernoulli theory with a co-rotational coordinate system, defined from the structure space coordinate nodes, to refer the element equilibrium and motion equations. Geometric non-linear effects are considered, all associated with rigid body motions from the structure, under small strain hypothesis. In the riser motion, the influences of its own weight, buoyancy forces, hydrodynamic loadings due to the maritime currents, the prescribed displacements at the top point line, the inertia forces and the floating action are considered. Effects on the line associated to the seabed contact are considered using Lagrange multipliers. They represent, the required loading (forces and moments) to ensure the cable geometric restrictions. In the model, friction forces effects on the seabed are not considered and the seabed stiffness is taken much greater than the riser s. The beam model stiffness matrix results into an increased matrix to accommodate the new model unknowns reactions, which are represented by the contact forces and moments. Similarly, conditions for variable contact and/or separation, as well as large relative motions between the flexible line and the seabed, are contemplated by the model. Solutions of the resulting nonlinear motion equations are obtained using Newmark s step-by-step time integration procedure with the Newton-Raphson iterative technique, for the numerical solution convergence. The methodology has been implemented and some representative offshore engineering testing analysis results are presented compared to other independently published solutions.

[pt] Esta tese apresenta uma nova metodologia para a avaliação de índices de freqüência e duração (FeD) em estudos de confiabilidade composta geração e transmissão de sistemas de potência de grande porte. Os índices FeD são obtidos através do método de simulação Monte Carlo não seqüencial. São desenvolvidas duas técnicas de Lagrange associados à análise de desempenho de cada estado são utilizados para identificar a fronteira que separa os estados de falha e sucesso do sistema. A segunda usa os conceitos de probabilidade condicional e coerência do sistema para caracterizar a contribuição de cada componente nos índices de freqüência. A primeira técnica também é utilizada no cálculo de limites superiores destes índices. A aplicação da metodologia é ilustrada através de estudos de casos com três sistemas, de 24, 120 e 500 barras, derivados de sistemas reais. os estudos indicam que ambas as técnicas se constituem em alternativas bastante atraentes para a estimação dos índices FeD. a primeira técnica mostrou-se ser cerca de 30% mais eficiente que a segunda, em termos computacionais. Por outro lado, a segunda técnica é mais flexível e, também, de implementação mais fácil. Viabiliza-se portanto, a aplicação prática de índices de freqüência e duração no planejamento integrado de sistemas geração/transmissão / [en] This thesis presents a new methodology for frequency and duration (FeD) assessment in composite generation and transmission reliability evaluation of large scale power systems. The FeD indices are obtained from a nonsequential Monte Carlo simulation scheme. Two tecniques are developed to estimate the feD indices. In the first, the Lagrange multipliers associated to the adequacy assessment of each state are used to identify the boundary wall between failure and success states. The second approach uses the concept of conditional probability and system coherence to caracterize the contribuition of each component to the frequency indices. Also, the first technique is used to calculate upper bounds of these indices. The methodology is illustrated in case studies with three test systems, with 24, 120 and 500 buses, derived from real systems. The studies indicated that both tecniques are very attractive in estimating the FeD índices. The first approach was about 30% faster than the second one. On the other hand, the second approach is more flexible and easy to implement. The proposed approach allows the pratical utilization of frequency and duration indices in integrates generation/transmission planning studies.

[pt] No atual modelo econômico do setor elétrico, é necessário identificar os agentes beneficiados pelos serviços ancilares à transmissão de potência de forma a alocar adequadamente os custos de investimento, de operação e manutenção do equipamento necessário para a prestação do serviço. Entre os serviços ancilares, destaca-se o suporte de potência reativa para a regulação de tensão. Este trabalho apresenta um método baseado nos multiplicadores de Lagrange de um problema de otimização associado ao cálculo das medidas corretivas necessárias para lidar com níveis de tensão inadequados. Dois critérios de otimização são definidos: mínimo corte de carga e mínima alocação de potência reativa. Os multiplicadores de Lagrange definem a responsabilidade de cada barra quando ocorrem violações de tensão no sistema. O método permite não só identificar as barras beneficiadas pelo equipamento de compensação de potência reativa como também alocar os custos entre elas. É priorizada a confiabilidade do sistema, analisando as contingências possíveis e considerando suas respectivas probabilidades de ocorrência. O programa computacional NH2, desenvolvido pelo CEPEL, é a ferramenta básica para o desenvolvimento deste trabalho. O método é aplicado, a título de ilustração, ao sistema IEEE - RTS de 24 barras e ao sistema da Área Rio. Os resultados obtidos são comparados com um método já existente, que define fatores de alocação de custos medindo os benefícios às barras devido ao suporte de potência reativa. Esta comparação, benefício x responsabilidade, e a própria teoria dos dois métodos, mostram que o método proposto identifica mais adequadamente as barras e os respectivos fatores para a repartição dos custos. / [en] It is important to identify the agents that take advantage of the ancillary services for system operation in the nowadays electricity market. The actual economic design requires that the costs of investment, operation and maintenance of the necessary equipment should be properly allocated between these agents. Among the ancillary services, the reactive power support for voltage regulation is quite important. It is presented a method that identifies the buses that take advantage of the reactive power equipment and allocates the costs between each one of them. The power system reliability is taken into account. The analysis considers possible contingencies and their respective probability of occurrence. The computer program NH2, developed by CEPEL, is the main tool for the development of this work. The method is based on the Lagrangian multipliers of an optimal power flow problem (OPF) associated to corrective measures necessary to deal with voltage violations. Two different objective functions are used: minimum load shedding and minimum reactive power injection. The Lagrangian multipliers define the responsibility of each bus when system voltage violations occur. For the purpose of illustration, the method is applied on the 24 bus IEEE Reliability Test System and on Área Rio system. Results are compared with those produced by other existing method that defines cost allocation factors measuring the benefit due the reactive support. This comparison, benefit x responsibility, and the theory used by both methods, show that the proposed method identifies more appropriately the buses and the corresponding factors to allocate the costs.

This dissertation consists of 3 essays In the first essay, A Simple Variable Selection Technique for Nonlinear Models, written in cooperation with Timo Teräsvirta and Rolf Tschernig, I propose a variable selection method based on a polynomial expansion of the unknown regression function and an appropriate model selection criterion. The hypothesis of linearity is tested by a Lagrange multiplier test based on this polynomial expansion. If rejected, a kth order general polynomial is used as a base for estimating all submodels by ordinary least squares. The combination of regressors leading to the lowest value of the model selection criterion is selected.  The second essay, Modelling and Forecasting Economic Time Series with Single Hidden-layer Feedforward Autoregressive Artificial Neural Networks, proposes an unified framework for artificial neural network modelling. Linearity is tested and the selection of regressors performed by the methodology developed in essay I. The number of hidden units is detected by a procedure based on a sequence of Lagrange multiplier (LM) tests. Serial correlation of errors and parameter constancy are checked by LM tests as well. A Monte-Carlo study, the two classical series of the lynx and the sunspots, and an application on the monthly S&amp;P 500 index return series are used to demonstrate the performance of the overall procedure. In the third essay, Forecasting with Artificial Neural Network Models (in cooperation with Marcelo Medeiros), the methodology developed in essay II, the most popular methods for artificial neural network estimation, and the linear autoregressive model are compared by forecasting performance on 30 time series from different subject areas. Early stopping, pruning, information criterion pruning, cross-validation pruning, weight decay, and Bayesian regularization are considered. The findings are that 1) the linear models very often outperform the neural network ones and 2) the modelling approach to neural networks developed in this thesis stands up well with in comparison when compared to the other neural network modelling methods considered here. / <p>Diss. Stockholm : Handelshögskolan, 2002. Spikblad saknas</p>

This thesis consists of four research papers. The main focus is on building the multivariate Conditional Correlation (CC-) GARCH models. In particular, emphasis lies on considering an extension of CC-GARCH models that allow for interactions or causality in conditional variances. In the first three chapters, misspecification testing and parameter restrictions in these models are discussed. In the final chapter, a computer package for building major variants of the CC-GARCH models is presented. The first chapter contains a brief introduction to the CC-GARCH models as well as a summary of each research paper. The second chapter proposes a misspecification test for modelling of the conditional variance part of the Extended Constant CC-GARCH model. The test is designed for testing the hypothesis of no interactions in the conditional variances. If the null hypothesis is true, then the conditional variances may be described by the standard CCC-GARCH model. The test is constructed on the Lagrange Multiplier (LM) principle that only requires the estimation of the null model. Although the test is derived under the assumption of the constant conditional correlation, the simulation experiments suggest that the test is also applicable to building CC-GARCH models with changing conditional correlations. There is no asymptotic theory available for these models, which is why simulation of the test statistic in this situation has been necessary. The third chapter provides yet another misspecification test for modelling of the conditional variance component of the CC-GARCH models, whose parameters are often estimated in two steps. The estimator obtained through these two steps is a two-stage quasi-maximum likelihood estimator (2SQMLE). Taking advantage of the asymptotic results for 2SQMLE, the test considered in this chapter is formulated using the LM principle, which requires only the estimation of univariate GARCH models. It is also shown that the test statistic may be computed by using an auxiliary regression. A robust version of the new test is available through another auxiliary regression. All of this amounts to a substantial simplification in computations compared with the test proposed in the second chapter. The simulation experiments show that, under both under both Gaussian and leptokurtic innovations, as well as under changing conditional correlations, the new test has reasonable size and power properties. When modelling the conditional variance, it is necessary to keep the sequence of conditional covariance matrices positive definite almost surely for any time horizon. In the fourth chapter it is demonstrated that under certain conditions some of the parameters of the model can take negative values while the conditional covariance matrix remains positive definite almost surely. It is also shown that even in the simplest first-order vector GARCH representation, the relevant parameter space can contain negative values for some parameters, which is not possible in the univariate model. This finding makes it possible to incorporate negative volatility spillovers into the CC-GARCH framework. Many new GARCH models and misspecification testing procedures have been recently proposed in the literature. When it comes to applying these models or tests, however, there do not seem to exist many options for the users to choose from other than creating their own computer programmes. This is especially the case when one wants to apply a multivariate GARCH model. The last chapter of the thesis offers a remedy to this situation by providing a workable environment for building CC-GARCH models. The package is open source, freely available on the Internet, and designed for use in the open source statistical environment R. With this package can estimate major variants of CC-GARCH models as well as simulate data from the CC-GARCH data generating processes with multivariate normal or Student's t innovations. In addition, the package is equipped with the necessary functions for conducting diagnostic tests such as those discussed in the third chapter of this thesis. / <p>Diss. Stockholm : Handelshögskolan, 2010. Sammanfattning jämte 4 uppsatser.</p>

Diss. Stockholm : Handelshögskolan, 2002.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-19T12:53:20Z No. of bitstreams: 1 raphaelpaulobragapoubel.pdf: 1692665 bytes, checksum: e8fb69a9681a9af78d618fd006ce0ebd (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-12-19T13:07:51Z (GMT) No. of bitstreams: 1 raphaelpaulobragapoubel.pdf: 1692665 bytes, checksum: e8fb69a9681a9af78d618fd006ce0ebd (MD5) / Made available in DSpace on 2016-12-19T13:07:51Z (GMT). No. of bitstreams: 1 raphaelpaulobragapoubel.pdf: 1692665 bytes, checksum: e8fb69a9681a9af78d618fd006ce0ebd (MD5) Previous issue date: 2012-02-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho apresenta um modelo baseado em métodos heurísticos construtivos para solução do planejamento dinâmico de linhas de transmissão. O acoplamento temporal entre as decisões é representado através de uma modificação nas equações do modelo de fluxo de carga CC onde as perdas nas linhas são incluídas. O problema resultante desta formulação é um problema de otimização inteira com variáveis acopladas no período de planejamento representadas por um parâmetro de expansão. O algoritmo proposto resolve o problema de forma contínua e acoplada para decidir sobre o planejamento de cada ano de forma a evitar a explosão combinatória da programação inteira. Para tanto são utilizadas, para as decisões de expansão, as informações dos coeficientes de Lagrange e do parâmetro de expansão. Testes com o sistema da região Sul e Sudeste do Brasil apontam para uma metodologia eficaz e promissora. / This work presents a model to solve the dynamic planning of transmission lines based on heuristics technique. The temporal coupling among decisions is represented by a modification on the equations of the DC load flow model, in which losses in transmission lines are included. This formulation generates an integer optimization problem with coupled variables in the planning period, represented by an expansion parameter. The proposed algorithm solves the problem in a continuous and coupled way, in order to decide the planning of each year, as well as to avoid combinatorial explosion of the integer technique. Information obtained from the Lagrange multiplier and the expansion parameter are used to take decisions. Tests with Brazilian southern and southeastern systems indicate an effective and promising methodology.

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.