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It is felt the position of the Scheffé polynomials as the primary, or sometimes sole recourse for practitioners of mixture experiments leads to a lack of enquiry regarding the type of blending behaviour that is used to describe the response and that this could be detrimental to achieving experimental objectives. Consequently, a new class of models and new experimental designs are proposed allowing a more thorough exploration of the experimental region with respect to different blending behaviours, especially those not associated with established models for mixtures, in particular the Scheffé polynomials. The proposed General Blending Models for Mixtures (GBMM) are a powerful tool allowing a broad range of blending behaviour to be described. These include those of the Scheffé polynomials (and its reparameterisations) and Becker's models. The potential benefits to be gained from their application include greater model parsimony and increased interpretability. Through this class of models it is possible for a practitioner to reject the assumptions inherent in choosing to model with the Scheffé polynomials and instead adopt a more open approach, flexible to many different types of behaviour. These models are presented alongside a fitting procedure, implementing a stepwise regression approach to the estimation of partially linear models with multiple nonlinear terms. The new class of models has been used to develop designs which allow the response surface to be explored fully with respect to the range of blending behaviours the GBMM may describe. These designs may additionally be targeted at exploring deviation from the behaviour described by the established models. As such, these designs may be thought to possess an enhanced optimality with respect to these models. They both possess good properties with respect to optimality criterion, but are also designed to be robust against model uncertainty.

System identification deals with the estimation of mathematical models from experimental data. As mathematical models are built for specific purposes, ensuring that the estimated model represents the system with sufficient accuracy is a relevant aspect in system identification. Factors affecting the accuracy of the estimated model include the experimental data, the manner in which the estimation method accounts for prior knowledge about the system, and the uncertainties arising when designing the experiment and initializing the search of the estimation method. As the accuracy of the estimated model depends on factors that can be affected by the user, it is of importance to guarantee that the user decisions are optimal. Hence, it is of interest to explore how to optimally perform an experiment in the system, how to account for prior knowledge about the system and how to deal with uncertainties that can potentially degrade the model accuracy. This thesis is divided into three topics. The first contribution concerns an input design framework for the identification of nonlinear dynamical models. The method designs an input as a realization of a stationary Markov process. As the true system description is uncertain, the resulting optimization problem takes the uncertainty on the true value of the parameters into account. The stationary distribution of the Markov process is designed over a prescribed set of marginal cumulative distribution functions associated with stationary processes. By restricting the input alphabet to be a finite set, the parametrization of the feasible set can be done using graph theoretical tools. Based on the graph theoretical framework, the problem formulation turns out to be convex in the decision variables. The method is then illustrated by an application to model estimation of systems with quantized measurements. The second contribution of this thesis is on Bayesian techniques for input design and estimation of dynamical models. In regards of input design, we explore the application of Bayesian optimization methods to input design for identification of nonlinear dynamical models. By imposing a Gaussian process prior over the scalar cost function of the Fisher information matrix, the method iteratively computes the predictive posterior distribution based on samples of the feasible set. To drive the exploration of this set, a user defined acquisition function computes at every iteration the sample for updating the predictive posterior distribution. In this sense, the method tries to explore the feasible space only on those regions where an improvement in the cost function is expected. Regarding the estimation of dynamical models, this thesis discusses a Bayesian framework to account for prior information about the model parameters when estimating linear time-invariant dynamical models. Specifically, we discuss how to encode information about the model complexity by a prior distribution over the Hankel singular values of the model. Given the prior distribution and the likelihood function, the posterior distribution is approximated by the use of a Metropolis-Hastings sampler. Finally, the existence of the posterior distribution and the correctness of the Metropolis-Hastings sampler is analyzed and established. As the last contribution of this thesis, we study the problem of uncertainty in system identification, with special focus in input design. By adopting a risk theoretical perspective, we show how the uncertainty can be handled in the problems arising in input design. In particular, we introduce the notion of coherent measure of risk and its use in the input design formulation to account for the uncertainty on the true system description. The discussion also introduces the conditional value at risk, which is a risk coherent measure accounting for the mean behavior of the cost function on the undesired cases. The use of risk coherent measures is also employed in application oriented input design, where the input is designed to achieve a prescribed performance in the intended model application. / <p>QC 20161216</p>

Recent advances in wireless communication industry, radio- frequency circuits are developing fast. For power amplifiers, the active circuits are mainly composed of transistors where withstand high voltage and current. The excellent transistors characteristic result in good circuit performances. In the thesis, the modeling of InGaAs pseudomorphic high electron mobility transistor was provided by Win Semiconductor Corporation. The established small signal model contains extrinsic and intrinsic elements. The extrinsic elements are extracted by simple method without fitting process for long time. Then, the intrinsic elements are obtained by conventional matrix transformations. The each element of models is varied with different gate width area are also discussed. Finally, the nonlinear models are expanded upon the concept of small signal model. Due to some of intrinsic elements are significantly varied with bias, small signal models have not applied to nonlinear circuit simulations. For developing nonlinear models, the nonlinear elements characteristics are described by empirical fitting equations. The accuracy of models is achieved by comparing simulated and on wafer measurement results, including DC¡Bsmall signal and large signal power characteristics.

The purpose of this thesis is to linearize a power amplifier using digital predistortion. A power amplifier is a nonlinear system, meaning that when fed with a pure input signal the output will be distorted. The idea behind digital predistortion is to distort the signal before feeding it to the power amplifier. The combined distortions from the predistorter and the power amplifier will then ideally cancel each other. In this thesis, two different approaches are investigated and implemented on an FPGA. The first approach uses a nonlinear model that tries to cancel out the nonlinearities of the power amplifier. The second approach is model-free and instead makes use of a look-up table that maps the input to a distorted output. Both approaches are made adaptive so that the parameters are continuously updated using adaptive algorithms. First the two approaches are simulated and tested thoroughly with different parameters and with a power amplifier model extracted from the real amplifier. The results are shown satisfactory in the simulations, giving good linearization for both the model and the model-free technique. The two techniques are then implemented on an FPGA and tested on the power amplifier. Even though the results are not as well as in the simulations, the system gets more linear for both the approaches. The results vary widely due to different circumstances such as input frequency and power. Typically, the distortions can be attenuated with around 10 dB. When comparing the two techniques with each other, the model-free method shows slightly better results.

This thesis firstly presents a nonlinear extended deterministic Susceptible-Infected (SI) model for assessing the impact of public health education campaign on curtailing the spread of the HIV pandemic in a population. Rigorous qualitative analysis of the model reveals that, in contrast to the model without education, the full model with education exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the effective reproduction number (Reff ), is less than unity. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden), and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries. The second problem considered is a Susceptible-Infected-Removed (SIR) model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For Case (i), we construct travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infected state or two endemic states with each other. For Case (ii), it is shown that the profile has the following properties: the number of susceptible individuals is monotone increasing and the number of infectives approaches zero, while their product converges to a constant. Numerical simulations are shown which confirm these analytical results. Abnormal behavior like travelling waves with non-monotone profile or oscillations are observed.

[pt] O principal objetivo desta dissertação é comparar o desempenho de modelos lineares e não-lineares de previsão de retornos de 23 ativos do mercado acionário americano. Propõe-se o modelo STAR-Tree Heterocedástico, que faz uso da metodologia do STAR-Tree (Smooth Transition AutoRegression Tree) aplicada a séries temporais heterocedásticas. Com a disponibilidade de dados de retorno e da volatilidade realizada de ações intra-diários, as séries de retornos são transformadas através da divisão de cada retorno pela sua volatilidade realizada. A série transformada apresenta variância constante. O modelo é uma combinação da metodologia STAR (Smooth Transition AutoRegression) e do algoritmo CART (Classification and Regression Tree). O modelo resultante pode ser interpretado como uma regressão de múltiplos regimes com transição suave. A especificação do modelo é feita através de testes de Multiplicadores de Lagrange, que indicam o nó a ser dividido e a variável de transição correspondente. Os modelos de comparação usados são o modelo Média, o método Naive, modelos lineares ARX e Redes Neurais. As previsões dos modelos foram avaliadas através de medidas estatísticas e financeiras. Os resultados financeiros baseam-se em uma regra de negociação automática que informa o momento de comprar e vender cada ativo. O modelo STAR-Tree Heterocedástico teve resultados estatísticos equivalentes aos dos outros modelos, porém apresentou um desempenho financeiro superior para a maioria das séries. A volatilidade realizada também foi estimada usando a metodologia STAR-Tree, e sua previsão foi utilizada para fazer uma análise de alavancagem financeira. / [en] The main goal of this dissertation is to compare the performance of linear and nonlinear models to forecast 23 assets of the American Stocks Market. The Heteroscedastic STAR-Tree Model is proposed using the STAR- Tree (Smooth Transition AutoRegression Tree) methodology applied to heteroscedastic time series. As assets returns and realized volatility intraday data are available, the returns series are transformed by dividing each return by its realized volatility, which gives homocedastic series. The model is a combination of the STAR (Smooth Transition AutoRegression) methodology and the CART (Classification and Regression Tree) algorithm. The resulting model can be interpreted as a smooth transition multiple regime regression. The model specification is done by Lagrange Multiplier tests that indicate the node to be split and the corresponding transition variable. The comparison models used are the Mean model, Naive method, ARX linear models and Neural Networks. The forecasting models were evaluated through statistical and financial measures. The financial results are based on an automatic trading rule that signals buy and hold moments in each stock. The Heteroscedastic STAR-Tree Model statistical performance was equivalent to the other models, however its financial performance was superior for most of the series. The STAR-Tree methodology was also applied for forecasting the realized volatility, and the forecasts were used in financial leverage analysis.

L’axe principal de la thèse est centré sur des approches non-linéaires modernes d’analyse des données économiques et financières, avec une attention particulière sur les cycles économiques et les crises financières. Un consensus dans la littérature statistique et financière s’est établie autour du fait que les variables économiques ont un comportement non-linéaire au cours des différentes phases du cycle économique. En tant que tel, les approches/modèles non-linéaires sont requis pour saisir les caractéristiques du mécanisme de génération des données intrinsèquement asymétriques, que les modèles linéaires sont incapables de reproduire.À cet égard, la thèse propose une nouvelle approche interdisciplinaire et ouverte à l’analyse des systèmes économiques et financiers. La thèse présente des approches robustes aux valeurs extrêmes et à la non-stationnarité, applicables à la fois pour des petits et de grands échantillons, aussi bien pour des séries temporelles économiques que financières. La thèse fournit des procédures dites étape par étape dans l’analyse des indicateurs économiques et financiers en intégrant des concepts basés sur la méthode de substitution de données, des ondelettes, espace incorporation de phase, la m´méthode retard vecteur variance (DVV) et des récurrences parcelles. La thèse met aussi en avant des méthodes transparentes d’identification, de datation des points de retournement et de l´évaluation des impacts des crises économiques et financières. En particulier, la thèse fournit également une procédure pour anticiper les crises futures et ses conséquences.L’étude montre que l’intégration de ces techniques dans l’apprentissage de la structure et des interactions au sein et entre les variables économiques et financières sera très utile dans l’élaboration de politiques de crises, car elle facilite le choix des méthodes de traitement appropriées, suggérées par les données.En outre, une nouvelle procédure pour tester la linéarité et la racine unitaire dans un cadre non-linéaire est proposé par l’introduction d’un nouveau modèle – le modèle MT-STAR – qui a des propriétés similaires au modèle ESTAR mais réduit les effets des problèmes d’identification et peut aussi représenter l’asymétrie dans le mécanisme d’ajustement vers l’équilibre. Les distributions asymptotiques du test de racine unitaire proposées sont non-standards et sont calculées. La puissance du test est évaluée par simulation et quelques illustrations empiriques sur les taux de change réel montrent son efficacité. Enfin, la thèse développe des modèles multi-variés Self-Exciting Threshold Autoregressive avec des variables exogènes (MSETARX) et présente une méthode d’estimation paramétrique. La modélisation des modèles MSETARX et des problèmes engendrés par son estimation sont brièvement examinés. / This thesis centers on introducing modern non-linear approaches for data analysis in economics and finance with special attention on business cycles and financial crisis. It is now well stated in the statistical and economic literature that major economic variables display non-linear behaviour over the different phases of the business cycle. As such, nonlinear approaches/models are required to capture the features of the data generating mechanism of inherently asymmetric realizations, since linear models are incapable of generating such behavior.In this respect, the thesis provides an interdisciplinary and open-minded approach to analyzing economic and financial systems in a novel way. The thesis presents approaches that are robust to extreme values, non-stationarity, applicable to both short and long data length, transparent and adaptive to any financial/economic time series. The thesis provides step-by-step procedures in analyzing economic/financial indicators by incorporating concepts based on surrogate data method, wavelets, phase space embedding, ’delay vector variance’ (DVV) method and recurrence plots. The thesis also centers on transparent ways of identifying, dating turning points, evaluating impact of economic and financial crisis. In particular, the thesis also provides a procedure on how to anticipate future crisis and the possible impact of such crisis. The thesis shows that the incorporation of these techniques in learning the structure and interactions within and between economic and financial variables will be very useful in policy-making, since it facilitates the selection of appropriate processing methods, suggested by the data itself.In addition, a novel procedure to test for linearity and unit root in a nonlinear framework is proposed by introducing a new model – the MT-STAR model – which has similar properties of the ESTAR model but reduces the effects of the identification problem and can also account for asymmetry in the adjustment mechanism towards equilibrium. The asymptotic distributions of the proposed unit root test is non-standard and is derived.The power of the test is evaluated through a simulation study and some empirical illustrations on real exchange rates show its accuracy. Finally, the thesis defines a multivariate Self–Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The modeling procedure for the MSETARX models and problems of estimation are briefly considered.

A produção de milho tem uma grande importância para o país. Ter o conhecimento sobre o crescimento da planta é de fundamental importância para seu manejo. Pode-se obter esse conhecimento fazendo um estudo por meio de modelos de crescimento, para se obter informações por meio de parâmetros com interpretações biológicas que trazem consigo um resumo sobre a curva característica do crescimento da planta, que podem ajudar no planejamento da cultura e principalmente conhecer qual período a planta mais cresce, a época mais adequada para adubação e realização do controle de pragas. Considerar características não comuns de suposições do modelo pode dar maior confiabilidade nos resultados do ajuste, como por exemplo a consideração da heterocedasticidade e não normalidade residual. Sendo assim, esse trabalho teve o objetivo de ajustar o modelo logístico considerando a heterocedasticidade e diferentes distribuições para o erro como normalidade, assimetria normal e assimetria t-student, a dados da altura da planta do milho do híbrido transgênico 30F35 Y (Yieldgard), observados ao longo do tempo. O experimento foi realizado no município de Votuporanga-SP, em área experimental do Pólo Regional Noroeste Paulista da APTA (Agência Paulista de Tecnologia dos Agro-negócios), no ano agrícola 2011/2012. A primeira medição da altura da planta de milho foi realizada 15 dias após a semeadura. As medições seguintes ocorreram com 30, 40, 50 e 122 dias, respectivamente, após a semeadura. Em cada dia de avaliação foi medido a altura das plantas em centímetros, com auxílio de uma régua, sendo esta medida da base da planta (solo) até o ápice da última folha expandida do cartucho. Toda a análise foi realizada utilizando o software R. Todos os modelos considerados se ajustaram bem a curva de crescimento do híbrido transgênico 30F35 Y (Yieldgard), porém o modelo logístico considerando erros normais assimétricos foi escolhido como mais adequado para modelar a curva, com base nos avaliadores utilizados. / Maize production is of great importance for the country. Knowing the plant development is of major importance to its management. Such knowledge may be attained through growth curves studies, to obtain information through parameters with biological interpretation which are able to synthesize the plantt\'s growth curve. This synthesis may help in management issues, such as information on the period of most rapid growth, best time to apply fertilizers and control pests. Considering uncommon features of the model assumptions may provide greater reliability on the results of the fitted model, such as residual heteroscedasticity and non-normality. In that sense, this work aimed to fit the logistic model considering variance heterogeneity and different error distributions such as normal, skew-normal and skew-t, to the transgenic hybrid 30F35Y maize height data through time. The experiment was conducted in the municipality of Votuporanga-SP, in an experimental station of the Pólo Regional Noroeste Paulista da Agência Paulista de Tecnologia dos Agro-Negócios (APTA) during the agronomic year of 2011/2012. The first height data measurement was taken 15 days after sewing. The following measurements were taken at 30, 40, 50 and 122 days after sewing. Each day the plant height was measured in centimeters using a ruler, measuring from the plant base (soil) until the edge of the last expanded leaf. All analyses were carried out using software R. All considered models fitted the data reasonably well, however the logistic model considering skew-normal errors was chosen as most adequate to model the data, basing on the goodness-of-fit tests.

Esta tese apresenta três ensaios empíricos sobre a relação entre comércio internacional e crescimento, utilizando modelos empíricos não lineares. No primeiro ensaio, os autores propõem o modelo MR-STVEC (Multiple Regime Smooth Transition VEC), para uma amostra de quatro países desenvolvidos (Estados Unidos, Canadá, Japão e Alemanha), na perspectiva de avaliar de que modo as exportações influenciam a produtividade total dos fatores (PFT). Os resultados indicam que as exportações possuem um mecanismo de reverter possíveis choques negativos de produtividade. Adicionalmente, para o Canadá e Alemanha, quando há um movimento de ascensão da produtividade, proveniente de um eventual choque positivo, as exportações também agem, mas de modo a restringi-lo. O segundo ensaio verifica a relação de causalidade entre variáveis de comércio internacional (exportações e importações) e a taxa de crescimento do produto, aqui mensurado pela produção industrial. Neste caso, a amostra é composta de vinte nações com diferentes níveis de renda. Uma abordagem empírica alternativa, denominada entropia de transferência (ET), é aplicada, com a vantagem de não assumir a priori qualquer tipo de especificação paramétrica. Os resultados mostram que o comércio internacional é um importante fator para melhor entender crescimento, em termos do conceito de redução de incertezas futura, com destaque para as exportações quando são considerados países em desenvolvimento. Entretanto, o sentido de causalidade reversa é predominante na amostra, em especial para países mais ricos. Por fim, o último ensaio segue o argumento de Hausmman et al (2007) e avalia se o grau de especialização das exportações e importações cria uma possível não linearidade entre abertura comercial e renda per capita. Em outras palavras: a composição da pauta de exportação e importação pode alterar a capacidade que a abertura comercial tem em explicar o diferencial de renda entre nações? Para verificar esta hipótese, aplica-se o modelo de painel com transição suave para 110 países, seguindo o mesmo procedimento Frankel e Romer (1999), evitando assim o problema de endogeneidade. Os resultados empíricos indicam que quando as exportações são especializadas em commodities e as importações são diversificadas, a abertura não é capaz de influenciar a renda. Por outro lado, se as exportações são mais diversificadas, independentemente do grau de especialização que as importações venham apresentar, a abertura torna-se relevante em explicar o diferencial de renda entre as nações. / The present dissertation is composed of three essays that study the relations between economic growth and international trade through nonlinear empirical models. In the first essay, the author uses Multiple Regimes Smooth Transition Vector Error-Correction Models (MR-STVEC) for a sample of developed countries (United States, Canada, Japan and Germany) in order to evaluate how exports may affect productivity. The results indicate that exports may reverse a drop of productivity. Furthermore, in particular for Canada and Germany, exports are able to restrict productivity when there is an ascent movement. The second essay examines the causality between foreign trade variables (exports and imports) and output growth, as measured by industrial production. Here, the sample is composed of twenty nations with different income levels. An alternative time series empirical approach called transfer entropy (ET) is applied; it does not impose any aprioristic parametric function. The results show that trade is an important factor for the understanding of output growth, particularly exports when we focus on some developing countries. However, the reverse causality is also observed and, in general, is preeminent. Finally, the last essay follows the arguments of Hausmman et al (2007) in order to verify if sectorial specialization of exports and imports creates nonlinearities between the degree of openness of an economy and its per capita income. In other words: the compositions of exports and imports can change the capacity that the economic degree of openness has to explain the income differentials among countries? In order to address this issue, the third essay applies a Panel Smooth Transition Model for 110 countries, following the same procedure of Frankel e Romer (1999) to avoid endogeneity problem. Results indicate that when exports are specialized in commodities and imports are diversified, openness do not influence income. Otherwise, if exports are diversified, independently of the levels of import\'s specialization, openness turns out to be relevant to explain per capita income.