This thesis consists of three distinct parts. Part I introduces the basic concepts and the notion of general quadratic term structures (GQTS) essential in some of the following chapters. Part II focuses on credit risk models and Part III studies forward price term structure models using both the classical and the geometrical approach.  Part I is organized as follows. Chapter 1 is divided in two main sections. The first section presents some of the fundamental concepts which are a pre-requisite to the papers that follow. All of the concepts and results are well known and hence the section can be regarded as an introduction to notation and the basic principles of arbitrage theory. The second part of the chapter is of a more technical nature and its purpose is to summarize some key results on point processes or differential geometry that will be used later in the thesis. For finite dimensional factor models, Chapter 2 studies GQTS. These term structures include, as special cases, the affine term structures and Gaussian quadratic term structures previously studied in the literature. We show, however, that there are other, non-Gaussian, quadratic term structures and derive sufficient conditions for the existence of these GQTS for zero-coupon bond prices. On Part II we focus on credit risk models.   In Chapter 3 we propose a reduced form model for default that allows us to derive closed-form solutions for all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and survival probabilities. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity of default is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds. Further on, we study a model for portfolio credit risk that considers both firm-specific and systematic risk. The model generalizes the attempt of Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering effects. Next, we show how to price CDOs, options on CDOs and how to incorporate the link to currently proposed credit indices. In Chapter 4 we start by presenting a reduced-form multiple default type of model and derive abstract results on the influence of a state variable $X$ on credit spreads when both the intensity and the loss quota distribution are driven by $X$. The aim is to apply the results to a real life situation, namely, to the influence of macroeconomic risks on the term structure of credit spreads. There is increasing support in the empirical literature for the proposition that both the probability of default (PD) and the loss given default (LGD) are correlated and driven by macroeconomic variables. Paradoxically, there has been very little effort, from the theoretical literature, to develop credit risk models that would take this into account. One explanation might be the additional complexity this leads to, even for the ``treatable'' default intensity models. The goal of this paper is to develop the theoretical framework necessary to deal with this situation and, through numerical simulation, understand the impact of macroeconomic factors on the term structure of credit spreads. In the proposed setup, periods of economic depression are both periods of higher default intensity and lower recovery, producing a business cycle effect. Furthermore, we allow for the possibility of an index volatility that depends negatively on the index level and show that, when we include this realistic feature, the impacts on the credit spread term structure are emphasized. Part III studies forward price term structure models. Forward prices differ from futures prices in stochastic interest rate settings and become an interesting object of study in their own right. Forward prices with different maturities are martingales under different forward measures. This mathematical property implies that the term structure of forward prices is always linked to the term structure of bond prices, and this dependence makes forward price term structure models relatively harder to handle. For finite dimensional factor models, Chapter 5 applies the concept of GQTS to the term structure of forward prices. We show how the forward price term structure equation depends on the term structure of bond prices. We then exploit this connection and show that even in quadratic short rate settings we can have affine term structures for forward prices. Finally, we show how the study of futures prices is naturally embedded in the study of forward prices, that the difference between the two term structures may be deterministic in some (non-trivial) stochastic interest rate settings. In Chapter 6 we study a fairly general Wiener driven model for the term structure of forward prices. The model, under a fixed martingale measure, $\Q$, is described by using two infinite dimensional stochastic differential equations (SDEs). The first system is a standard HJM model for (forward) interest rates, driven by a multidimensional Wiener process $W$. The second system is an infinite SDE for the term structure of forward prices on some specified underlying asset driven by the same $W$. Since the zero coupon bond volatilities will enter into the drift part of the SDE for these forward prices, the interest rate system is needed as input to the forward price system. Given this setup, we use the Lie algebra methodology of Bj\o rk et al. to investigate under what conditions, on the volatility structure of the forward prices and/or interest rates, the inherently (doubly) infinite dimensional SDE for forward prices can be realized by a finite dimensional Markovian state space model. / Diss. Stockholm : Handelshögskolan, 2006

This thesis provides more precise characterisation of patterns, causes and consequences of takeover activity in Australia over three decades spanning from 1972 to 2004. The first contribution of the thesis is to characterise the time series behaviour of takeover activity. It is found that linear models do not adequately capture the structure of merger activity; a non-linear two-state Markov switching model works better. A key contribution of the thesis is, therefore, to propose an approach of combining a State-Space model with the Markov switching regime model in describing takeover activity. Experimental results based on our approach show an improvement over other existing approaches. We find four waves, one in the 1980s, two in the 1990s, and one in the 2000s, with an expected duration of each wave state of approximately two years. The second contribution is an investigation of the extent to which financial and macro-economic factors predict takeover activity after controlling for the probability of takeover waves. A main finding is that while stock market boom periods are empirically associated with takeover waves, the underlying driver is interest rate level. A low interest rate environment is associated with higher aggregate takeover activity. This relationship is consistent with Shleifer and Vishny (1992)'s liquidity argument that takeover waves are symptoms of lower cost of capital. Replicating the analysis to the biggest takeover market in the world, the US, reveals a remarkable consistency of results. In short, the Australian findings are not idiosyncratic. Finally, the implications for target and bidder firm shareholders are explored via investigation of takeover bid premiums and long-term abnormal returns separately between the wave and non-wave periods. This represents the third contribution to the literature of takeover waves. Findings reveal that target shareholders earn abnormally positive returns in takeover bids and bid premiums are slightly lower in the wave periods. Analysis of the returns to bidding firm shareholders suggests that the lower premiums earned by target shareholders in the wave periods may simply reflect lower total economic gains, at the margin, to takeovers made in the wave periods. It is found that bidding firms earn normal post-takeover returns (relative to a portfolio of firms matched in size and survival) if their bids are made in the non-wave periods. However, bidders who announce their takeover bids during the wave periods exhibit significant under-performance. For mergers that took place within waves, there is no difference in bid premiums and nor is there a difference in the long-run returns of bidders involved in the first half and second half of the waves. We find that none of theories of merger waves (managerial, mis-valuation and neoclassical) can fully account for the Australian takeover waves and their effects. Instead, our results suggest that a combination of these theories may provide better explanation. Given that normal returns are observed for acquiring firms, taken as a whole, we are more likely to uphold the neoclassical argument for merger activity. However, the evidence is not entirely consistent with neo-classical rational models, the under-performance effect during the wave states is consistent with the herding behaviour by firms.

[pt] Esta tese apresente duas contribuições para a modelagem e previsão de sinistros já ocorridos e ainda não avisados (Incurred But Not Reported – IBNR), quando organizados numa estrutura de dados conhecida como triângulo de run-off. Ambas as contribuições são baseadas em arcabouços gerais para a construção de modelos para séries temporais com coeficientes variantes no tempo. Em nossa primeira contribuição desenvolvemos a extensão multivariada do modelo em espaço de estado proposto por Atherino em 2008. A partir dessa extensão é possível modelas simultaneamente um ou mais triângulos de run-off associados às diversas coberturas de uma seguradora, levando-se em consideração a dependência entre os distintos triângulos, capturada pela estrutura da matriz variância – covariância do modelo SUTSE e a dependência entre as células de cada triângulo de run-off, capturada pelas componentes de nível e de periodicidade, de acordo com a proposta de atherino et al. (2010). Em nossa segunda contribuição desenvolvemos um arcabouço geral para a modelagem univariada de triângulos de run-off a partir da estruturas dos modelos GAS (Generalized Autoregressive Score) desenvolvidos por Creal at al. (2013). Esse arcabouço, bastante flexível, permite a escolha de qualquer distribuição para as entradas do triângulo run-off, considerando que os seus parâmetros variem ao longo período de origem ou de desenvolvimento. Em particular consideramos as distribuições gama e log-normal. Nossos resultados foram comparados com os obtidos através do método chain ladder (Mack, 1993), utilizado como benchmark na indústria de seguros. O teste Diebold e Mariano (1995) evidenciou que os modelos propostos geram melhores previsões, comparadas as previsões do método chain ladder. / [en] This thesis presents two contributions to the modeling and prediction of a type of claims in the insurance industry known as IBNR (Incurred But Not Reported) when these are organized in a data structure known as the run-off triangle. Both contributions are based on general frameworks for building models for time series with time varying coefficients. In our first contribution we developed the multivariate extension of the state space model proposed by Atherino in 2008. From this extension it is possible to model simultaneously one or more run-off triangles associated with different coverages from an insurer, taking into account the dependence between different triangles, captured by the structure of the variance-covariance matrix of the SUTSE model, while the dependence between the cells of each triangle run-off is captured by the components of level and periodicity according to the model proposed by Atherino (2008). In our second contribution we developed a general framework for univariate modeling of run-off triangles using the structure of GAS models (Generalized Autoregressive Score) developed by Creal et al. (2013). This framework, very flexible, allows one to choose any distribution to the inputs of the triangle run-off, considering that its parameters can vary over the period of origin or period of development. In particular we have considered both gamma and lognormal distributions. Our results were compared with those obtained by the chain ladder method (Mack, 1993) used as a benchmark in the insurance industry. The Diebold and Mariano test (1995) showed that the proposed models produced better predictions compared to the predictions of the chain ladder method.

No description available.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-09T17:52:47Z No. of bitstreams: 1 CARLOS ANTONIO PEREIRA DA SILVA - DISSERTAÇÃO PPGMAT 2014..pdf: 597533 bytes, checksum: 741e2e32988fe89dd00df90b6aa0c5c9 (MD5) / Made available in DSpace on 2018-08-09T17:52:47Z (GMT). No. of bitstreams: 1 CARLOS ANTONIO PEREIRA DA SILVA - DISSERTAÇÃO PPGMAT 2014..pdf: 597533 bytes, checksum: 741e2e32988fe89dd00df90b6aa0c5c9 (MD5) Previous issue date: 2014-08 / Capes / Neste trabalho, como uma aplicação adequada do bem conhecido Princípio do Máximo Generalizado de Omori-Yau, obtemos resultados relativos a rigidez para hipersuperfícies tipo-espaço completas imersas na metade Hn+1 do espaço de De Sitter Sn+11 , que é chamado de steady state space. Por outro lado, usando uma isometria equivalente para o modeloHn+1, estenderemos nossos resultados a uma família maior de espaços-tempos. Por fim, estudaremos também a singularidade de gráficos verticais inteiros nesses espaços-tempos ambiente. / In this work, as a suitable application of the well known generalized Maximum Principle of Omori-Yau, we obtain rigidity results concerning to complete spacelike hypersurfaces immersed in the half Hn+1 of the de Sitter spaceSn+11 , which models the so-called steady state space. Moreover, by using an isometrically equivalent model for Hn+1, we extend our results to a wider family of spacetimes. Finally, we also study the uniqueness of entire vertical graphs in such ambient spacetimes.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-30T14:13:06Z No. of bitstreams: 1 RAFAEL BEZERRA CORREIA LIMA - TESE PPGEE 2016..pdf: 2324960 bytes, checksum: db1b63193864e8e19bcba191952df2b9 (MD5) / Made available in DSpace on 2018-07-30T14:13:06Z (GMT). No. of bitstreams: 1 RAFAEL BEZERRA CORREIA LIMA - TESE PPGEE 2016..pdf: 2324960 bytes, checksum: db1b63193864e8e19bcba191952df2b9 (MD5) Previous issue date: 2016-09-20 / Nesse trabalho são apresentadas contribuições na área de identificação de sistemas representados em espaço de estados. E proposta uma metodologia completa para estimação de modelos que representem as principais dinâmicas de processos industriais. O fluxo natural das procedimentos de identificação consiste da coleta experimental dos dados, seguido pela escolha dos modelos candidatos e da utilização de um critério de ajuste que selecione o melhor modelo possível. Nesse sentido é proposta uma metodologia para estimativa de modelos em espaço de estados, utilizando excitações pulsadas. A abordagem desenvolvida combina algoritmos precisos e eficientes com experimentos rápidos, adequados a ambientes industriais. O projeto das excitações é realizado em tempo real, por meio de informações coletadas em um curto experimento inicial, baseado em uma única oscilação de uma estrutura realimentada por um relê. Esse mecanismo possibilita uma estimativa preliminar do atraso e da constante de tempo dominante do sistema. O método de identificação proposto é baseado na teoria de realizações de Kalman. É apresentada uma reformulação do problema de realizações clássico, para comportar sinais de entrada pulsados. Essa abordagem se mostra computacionalmente eficiente, assim como apresenta resultados semelhantes aos métodos de benehmark. A técnica possibilita também a estimativa de atrasos de transporte e a inserção de conhecimentos prévios por meio de um problema de otimização com restrições via LMI Linear Matrix Incqualities. Em muitos casos, somente as características principais do sistema são relevantes em um projeto de sistema de controle. Portanto é proposta uma técnica para obtenção de modelos de primeira ordem com atraso, a partir da redução de modelos balanceados em espaço de estados. Por fim, todas as contribuições discutidas nesse trabalho de tese são validadas em uma série de plantas experimentais em escala de laboratório. Plantas essas, projetadas e construídas com o intuito de emular o cotidiano operacional de instalações industriais reais. / This work Íntroduces contributions related to thc field of systems identification of state space models. It is proposed a complete methodology for modei estimation that encompasses the main dynamics of industrial processes. The natural flxix of the identification procedures rests on the the empirical collection of data followed by the choice of candidate modela and posterior use ot an adjusting criteria that drafts the best model amoug the contenders. In this sense. a uew methodology is proposed for models estimation in state spaces using pulsed excitation signal. The developed approach combines accurate and efhcient algorithms with quick experíments whose are suitable for the industrial environment. The excitatiou design is performed in real time by means of information collected in a snort mitíai experíment based in an single oscillation of a relay feedback. This mechanism allows a preliminary estimation of both delay and time constant prevalent in the system. The identification method proposed is based on Kalmairs realization theory. The thesis íntroduces a reformulation of the classic realization problem so it can admit pulsed input signals. This approaíth show itself as computationally efficient as well as provides similar results eompared to those obtained when perfonning the benchmark methods. Moreover, the technic allows the transport delay estimation and insertion of prior knowledge by means of an optimization problem with restrictions via linear matrix inequalities restrictions. In many cases only the characteristics of the main system are relevant in control systems design. Therefore a technique for the attainment first order models with time delay based on balanced state space models reduction. Lastly ali the contributions provided aíong the thesis are discussed and validated in a series of pilot scale plants. designed and built to emulate the operational cycle in real industrial plants.

Submitted by Rafael da Rocha Mendonça Bacciotti (rafael.bacciotti@gmail.com) on 2017-08-13T23:42:30Z No. of bitstreams: 1 Rafael Bacciotti_defesa.pdf: 1094193 bytes, checksum: 7a7f6313d22efa00eb4133077c507ec5 (MD5) / Rejected by Joana Martorini (joana.martorini@fgv.br), reason: Falta a ficha catalográfica. on 2017-08-14T13:23:19Z (GMT) / Submitted by Rafael da Rocha Mendonça Bacciotti (rafael.bacciotti@gmail.com) on 2017-08-21T18:34:28Z No. of bitstreams: 1 Rafael Bacciotti_final.pdf: 959318 bytes, checksum: a65761f39f40377669fe2d34280903ab (MD5) / Approved for entry into archive by Joana Martorini (joana.martorini@fgv.br) on 2017-08-21T18:55:31Z (GMT) No. of bitstreams: 1 Rafael Bacciotti_final.pdf: 959318 bytes, checksum: a65761f39f40377669fe2d34280903ab (MD5) / Made available in DSpace on 2017-08-22T12:21:28Z (GMT). No. of bitstreams: 1 Rafael Bacciotti_final.pdf: 959318 bytes, checksum: a65761f39f40377669fe2d34280903ab (MD5) Previous issue date: 2017-08-11 / A análise do mercado de trabalho em perspectiva histórica com base em séries de alta frequência no Brasil é uma tarefa desafiadora, pois não há uma pesquisa longa, abrangente e ao mesmo tempo compatível em termos metodológicos e conceituais que permita acompanhar o desempenho das diversas variáveis de maneira adequada. Essas questões foram exacerbadas no início de 2016, quando a Pesquisa Mensal de Emprego (PME) foi interrompida pelo IBGE. Desde então, a Pesquisa Nacional por Amostra de Domicílios Contínua (PNAD Contínua) passou a ser a única referência do instituto sobre o mercado de trabalho em alta frequência. Nesse contexto, este trabalho tem como objetivo retroagir a taxa de desemprego trimestral da Pesquisa Nacional por Amostra de Domicílios Contínua (PNAD Contínua), iniciada em março de 2012. Duas séries foram geradas com base na metodologia de modelos de espaço de estados e o filtro de Kalman: a primeira iniciada em 1976 e outra em 1984, utilizando-se como referência, nos dois casos, as taxas de desemprego obtidas na PNAD anual e na Pesquisa de Emprego e Desemprego (PED - Dieese). / The analysis of the labor market in historical perspective in Brazil is a challenging task, since there is not a long, comprehensive and at the same time methodologically and conceptually compatible survey that allows monitoring the performance of the various variables in an appropriate manner. These issues were exacerbated in early 2016, when the Pesquisa Mensal de Emprego (PME) was interrupted by IBGE. Since then, the Pesquisa Nacional por Amostra de Domicílios Contínua (PNAD Contínua) has become the Institute's only reference to the high-frequency labor market monitoring. In this context, the objective of this study is to retropolate the unemployment rate from PNAD Contínua, begun in March 2012. Two series were produced from the state space model methodology, with the Kalman filter, one since 1976 and another since 1984, using as reference the annual PNAD and the Pesquisa de Emprego e Desemprego (PED-Dieese).

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study. / Mathematical Sciences / M. Sc. (Statistics)

Made available in DSpace on 2014-06-11T19:22:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-08-27Bitstream added on 2014-06-13T19:28:00Z : No. of bitstreams: 1 sampaio_lp_me_ilha.pdf: 1553174 bytes, checksum: 4a7ad1f1c4400135903509fd327b3112 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho propõe uma nova abordagem na metodologia de operação para o inversor Boost monofásico, como estrutura base para o aproveitamento de fontes alternativas e renováveis de energia elétrica. Considerando-se que equipamentos eletro/eletrônicos convencionais em CA (corrente alternada) necessitam, normalmente, de níveis e formato de tensão diferentes daqueles fornecidos por essas fontes de energia, o inversor proposto é uma estrutura integrada que tem a capacidade de operar como conversor elevador de tensão e inversor, apresentando um número reduzido de componentes e rendimento maior, quando comparado às formas tradicionais de se associar em cascata o conversor elevador com o inversor. O projeto convencional do inversor fonte de corrente (CSI) exige uma indutância elevada de entrada, além disso, o modelo a pequeno sinais do CSI é semelhante ao do conversor Boost no modo de condução contínua, apresentando um zero no semi-plano direito na função de transferência para o controle da tensão de saída, sendo que este zero causa o conhecido efeito de fase não-mínima. Desta forma, uma metodologia especial de projeto é apresentada resultando numa indutância Boost reduzida e numa técnica de controle utilizando um sistema multi-malhas, com alimentação direta, devidamente projetada de forma a possibilitar elevadas dinâmicas de transferência de energia. Adicionalmente, o inversor apresenta tensão de saída com reduzidas distorções harmônicas (DHT), número reduzido de componentes de potência e, consequentemente, elevada densidade de potência. Neste trabalho são apresentadas as análises qualitativa e quantitativa do inversor, a modelagem e técnica de controle proposta, metodologia de projeto, os principais resultados de simulação e experimentais com a finalidade de demonstrar a viabilidade de aplicação da proposta. / This work presents a new methodology for the operation and control of a single-phase current-source Boost Inverter, it is used as base structure for alternative and renewable electric energy sources. The electro/electronics devices normally require eletrical source in AC (alternate current) in different voltage levels and shapes those provided by the alternative and renewable electrical sources. The proposed inverter is an integrated structure able to operate as step-up DC-DC converter and inverter, it presents a reduced number of components, high efficiency when compared with the traditional technique of step-up and inverter for cascade association. The conventional design of current source inverter (CSI) require a large boost inductance, therefore, the small-signal model is similar to continuous-current-mode (CCM) Boost converter, which has a right-half-plane (RHP) zero in its control-to-output transfer function, and this RHP zero causes the well-known non-minimum-phase effects. In this context, a special design with small boost inductance and a multi-loop control is proposed in order to assure stability and very fast dynamics. Furthermore, the inverter presents output voltage with very low total harmonic distortion (THD), reduced number of components and high power density. In addition, this work presents the Boost CSI operation, the proposed control technique, the main simulation and experimental results in order to demonstrate the feasibility of the proposal.

Submitted by JULIO CEZAR UZINSKI null (uzinski.jc@gmail.com) on 2016-12-15T21:43:22Z No. of bitstreams: 1 Uzinski JC.pdf: 2380247 bytes, checksum: 910b14a40501433136262e638e586b5f (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-12-20T16:20:21Z (GMT) No. of bitstreams: 1 uzinski_jc_dr_ilha.pdf: 2380247 bytes, checksum: 910b14a40501433136262e638e586b5f (MD5) / Made available in DSpace on 2016-12-20T16:20:21Z (GMT). No. of bitstreams: 1 uzinski_jc_dr_ilha.pdf: 2380247 bytes, checksum: 910b14a40501433136262e638e586b5f (MD5) Previous issue date: 2016-11-25 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Esta tese apresenta uma parametrização no espaço de estados para a transformada wavelet rápida. Esta parametrização é baseada em funções de base ortonormal e filtros de resposta finita ao impulso simultaneamente, uma vez que, a transformada rápida wavelet é um algoritmo que consiste em decompor sinais no domínio do tempo em sequências de coeficientes baseados numa base ortogonal de funções wavelet. Deste modo, vantagens apresentadas por ambas as propostas são incorporadas. Modelos de resposta finita ao impulso têm propriedades atrativas como vantagens computacionais e analíticas, garantia de estabilidade BIBO e robustez para a mudança de alguns parâmetros, dentre outras. Por outro lado, séries de funções de base ortonormal têm características que as fazem atrativas para a modelagem de sistemas dinâmicos, como ausência de recursão da saída, a não necessidade de se conhecer previamente a estrutura exata do vetor de regressão, possibilidade de aumentar a capacidade de representação do modelo aumentando-se o número de funções ortonormais utilizadas, desacoplamento natural das saídas em modelos multivariáveis; tolerância a dinâmicas não modeladas. Além disso, a realização no espaço de estados é mínima. A contribuição deste trabalho consiste no desenvolvimento de uma realização no espaço de estados para bancos de filtros wavelet, em que há a presença explícita de parâmetros que podem ser livremente ajustados mantendo as propriedades de reconstrução perfeita e ortonormalidade. Para ilustrar o funcionamento e as vantagens da técnica proposta, alguns exemplos de decomposição de sinais no contexto de processamento de sinais mostrando que ela proporciona os mesmos coeficientes wavelet que a transformada wavelet rápida, e uma aplicação em controle através de realimentação dinâmica de estados também são apresentados nesta tese. / This thesis presents a state-space parameterization for the fast wavelet transform. This parameterization is based on orthonormal basis functions and finite impulse response filters at the same time, since the fast wavelet transform is an algorithm, which converts a signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite wavelet functions. Advantages presented by both proposals are incorporated. Finite impulse response systems have attractive properties, for instance, computational and analytical advantages, BIBO stability and robustness guarantee to some parameter changes, and others. On the other hand, orthonormal basis functions have some characteristics that make them attractive for dynamic systems modeling, examples are, output recursion absence, not requiring prior regression vector exact structure knowledge; possibility of increasing the model representation capacity by increasing the number of orthonormal functions employed; natural outputs uncoupling in multivariable models; tolerance to unmodeled dynamics, and others. Furthermore, the state-space realization is minimal. The contribution of this work consists in the development of a state-space realization for a wavelet filter bank, with the explicit presence of the parameters that can be freely adjusted, keeping perfect-reconstruction and orthonormality guarantees. In order to illustrate advantages and how the proposed technique works, some decomposition examples in signal processing context are presented showing that it provides the same wavelet coefficients as the fast wavelet transform, and an application on dynamic state feedback control is also presented in this thesis. / CNPq: 160545/2013-7