This dissertation thesis is focused on the empirical analysis of monetary and fiscal policy using nonlinear models. In the first part, I examine the evolution of monetary policy rules in a group of inflation targeting countries. I apply a moment-based estimator in a time-varying parameter model with endogenous regressors. The main findings are twofold. First, with adoption of inflation targeting, coefficients in the monetary policy rules changed rather gradually. Second, the response of interest rates to inflation is particularly strong during periods when central bankers want to break a record of high inflation. Contrary to common view, the response of interest rates to inflation becomes less aggressive after the adoption of inflation targeting, suggesting a positive anchoring effect of this regime on inflation expectations. The second part discusses whether and how the selected central banks responded to episodes of financial stress over the last three decades. The time-varying monetary policy rule is extended for an indicator of financial stress, in order to show the departures of policy rules under financial instability. The findings suggest that central banks often decrease policy rates in the face of high financial stress. However, the size of the policy response varies substantially over time as well...

[pt] Os métodos de regressão baseados em árvores são modelos não lineares e não paramétricos, estudados desde a década de 80, quando houve a criação do algoritmo CART. Até hoje há muita pesquisa nessa área e cada vez mais novos métodos são apresentados com o objetivo de aperfeiçoar os modelos já existentes. Esse trabalho propõe um novo método chamado de Regressão Construtiva em Regiões Implícitas (RCRI). Sua principal diferença, com relação aos demais métodos baseados em árvores, está na forma como o domínio é particionado. Até o momento essa partição era formada por retângulos com arestas paralelas aos eixos, porém o algoritmo RCRI permitiu que as partições fossem formadas por regiões mais flexíveis definidas implicitamente. Além disso, o trabalho também propõe uma extensão intervalar para o modelo. Duas diferentes aplicações desse novo método também são sugeridas. A primeira em atuária, que busca melhorar a estimativa da reserva IBNR fornecida pelo já usual modelo Chain Ladder. A segunda em geologia, que utiliza as informações existentes nos poços para realizar inferências sobre dados faltantes. / [en] Tree-based methods are playing an important role in non-linear and non- parametric regression. They have been studied since the 80 s, when the CART algorithm was proposed. Nowadays there is a lot of research in this area and new methods are being created, aiming at improving existing models. This work proposes a new tree-based method called Constructive Regression on Implicit Regions. Its main difference, with respect to other tree-based methods, is how the domain is partitioned. The proposed algorithm allow s partitions formed by flexible regions whose borders are implicitly defined. Moreover, the work also proposes an interval extension to the model. Two different applications of this new method are also proposed. The first one is in actuary , which look s for improvements in the estimation of IBNR reserves, already provided by the usual Chain Ladder model. The second one is in geology , which uses the well data to perform inferences about the missing data in the well itself.

Le démélange spectral est un des sujets majeurs de l’analyse d’images hyperspectrales. Ce problème consiste à identifier les composants macroscopiques présents dans une image hyperspectrale et à quantifier les proportions (ou abondances) de ces matériaux dans tous les pixels de l’image. La plupart des algorithmes de démélange suppose un modèle de mélange linéaire qui est souvent considéré comme une approximation au premier ordre du mélange réel. Cependant, le modèle linéaire peut ne pas être adapté pour certaines images associées par exemple à des scènes engendrant des trajets multiples (forêts, zones urbaines) et des modèles non-linéaires plus complexes doivent alors être utilisés pour analyser de telles images. Le but de cette thèse est d’étudier de nouveaux modèles de mélange non-linéaires et de proposer des algorithmes associés pour l’analyse d’images hyperspectrales. Dans un premier temps, un modèle paramétrique post-non-linéaire est étudié et des algorithmes d’estimation basés sur ce modèle sont proposés. Les connaissances a priori disponibles sur les signatures spectrales des composants purs, sur les abondances et les paramètres de la non-linéarité sont exploitées à l’aide d’une approche bayesienne. Le second modèle étudié dans cette thèse est basé sur l’approximation de la variété non-linéaire contenant les données observées à l’aide de processus gaussiens. L’algorithme de démélange associé permet d’estimer la relation non-linéaire entre les abondances des matériaux et les pixels observés sans introduire explicitement les signatures spectrales des composants dans le modèle de mélange. Ces signatures spectrales sont estimées dans un second temps par prédiction à base de processus gaussiens. La prise en compte d’effets non-linéaires dans les images hyperspectrales nécessite souvent des stratégies de démélange plus complexes que celles basées sur un modèle linéaire. Comme le modèle linéaire est souvent suffisant pour approcher la plupart des mélanges réels, il est intéressant de pouvoir détecter les pixels ou les régions de l’image où ce modèle linéaire est approprié. On pourra alors, après cette détection, appliquer les algorithmes de démélange non-linéaires aux pixels nécessitant réellement l’utilisation de modèles de mélange non-linéaires. La dernière partie de ce manuscrit se concentre sur l’étude de détecteurs de non-linéarités basés sur des modèles linéaires et non-linéaires pour l’analyse d’images hyperspectrales. Les méthodes de démélange non-linéaires proposées permettent d’améliorer la caractérisation des images hyperspectrales par rapport au méthodes basées sur un modèle linéaire. Cette amélioration se traduit en particulier par une meilleure erreur de reconstruction des données. De plus, ces méthodes permettent de meilleures estimations des signatures spectrales et des abondances quand les pixels résultent de mélanges non-linéaires. Les résultats de simulations effectuées sur des données synthétiques et réelles montrent l’intérêt d’utiliser des méthodes de détection de non-linéarités pour l’analyse d’images hyperspectrales. En particulier, ces détecteurs peuvent permettre d’identifier des composants très peu représentés et de localiser des régions où les effets non-linéaires sont non-négligeables (ombres, reliefs,...). Enfin, la considération de corrélations spatiales dans les images hyperspectrales peut améliorer les performances des algorithmes de démélange non-linéaires et des détecteurs de non-linéarités. / Spectral unmixing is one the major issues arising when analyzing hyperspectral images. It consists of identifying the macroscopic materials present in a hyperspectral image and quantifying the proportions of these materials in the image pixels. Most unmixing techniques rely on a linear mixing model which is often considered as a first approximation of the actual mixtures. However, the linear model can be inaccurate for some specific images (for instance images of scenes involving multiple reflections) and more complex nonlinear models must then be considered to analyze such images. The aim of this thesis is to study new nonlinear mixing models and to propose associated algorithms to analyze hyperspectral images. First, a ost-nonlinear model is investigated and efficient unmixing algorithms based on this model are proposed. The prior knowledge about the components present in the observed image, their proportions and the nonlinearity parameters is considered using Bayesian inference. The second model considered in this work is based on the approximation of the nonlinear manifold which contains the observed pixels using Gaussian processes. The proposed algorithm estimates the relation between the observations and the unknown material proportions without explicit dependency on the material spectral signatures, which are estimated subsequentially. Considering nonlinear effects in hyperspectral images usually requires more complex unmixing strategies than those assuming linear mixtures. Since the linear mixing model is often sufficient to approximate accurately most actual mixtures, it is interesting to detect pixels or regions where the linear model is accurate. This nonlinearity detection can be applied as a pre-processing step and nonlinear unmixing strategies can then be applied only to pixels requiring the use of nonlinear models. The last part of this thesis focuses on new nonlinearity detectors based on linear and nonlinear models to identify pixels or regions where nonlinear effects occur in hyperspectral images. The proposed nonlinear unmixing algorithms improve the characterization of hyperspectral images compared to methods based on a linear model. These methods allow the reconstruction errors to be reduced. Moreover, these methods provide better spectral signature and abundance estimates when the observed pixels result from nonlinear mixtures. The simulation results conducted on synthetic and real images illustrate the advantage of using nonlinearity detectors for hyperspectral image analysis. In particular, the proposed detectors can identify components which are present in few pixels (and hardly distinguishable) and locate areas where significant nonlinear effects occur (shadow, relief, ...). Moreover, it is shown that considering spatial correlation in hyperspectral images can improve the performance of nonlinear unmixing and nonlinearity detection algorithms.

Submitted by (ana.araujo@ufrpe.br) on 2016-05-19T14:39:16Z No. of bitstreams: 1 Alessandro Henrique da Silva Santos.pdf: 536044 bytes, checksum: 011926984df2097b6901e78e8a50d28e (MD5) / Made available in DSpace on 2016-05-19T14:39:16Z (GMT). No. of bitstreams: 1 Alessandro Henrique da Silva Santos.pdf: 536044 bytes, checksum: 011926984df2097b6901e78e8a50d28e (MD5) Previous issue date: 2009-02-27 / The exponential family nonlinear models are an extension of the generalized models, opening various options for the distribution of the variable answer and allowing larger flexibility for the connection between the average and the systematic component. These models, for being less restrictive, having been used to model several phenomena in the nature. To estimate the parameters of these models, several procedures are proposed. Usually, the method of maximum likelihood, that has asymptotic properties of order n-1, where n is the size of the sample, it is the used. In this work we will make a general approach to the no-linear models of the exponential family. The theory of the exponential family will be introduced presenting the function of density of probability, function cumulantes geratriz, likelihood function, likelihood ratio and deviation of the model; such presented results will facilitate and/or they will be necessary in the understanding of what will be done for the nonlinear models of the exponential family. The exponential family nonlinear models will be defined by presenting the suppositions of the model, its likelihood function and the algorithm for the estimate of the parameters. We will make the approach of the diagnosis analysis and of influence of the exponential family nonlinear models. Finally, we will present some applications and we will show the efficiency and importance in the use of this class, once several phenomena present nonlinear behavior. / Os modelos não-lineares da família exponencial são uma extensão dos modelos generalizados, abrindo um leque de opções para a distribuição da variável resposta e permitindo maior flexibilidade para a ligação entre a média e a componente sistemática. Estes modelos, por serem menos restritivos, têm sido utilizados para modelar diversos fenômenos na natureza. Para estimar os parâmetros destes modelos, vários procedimentos são propostos. Usualmente, o método de máxima verossimilhança, que tem propriedades assintóticas de ordem n-1, onde n é o tamanho da amostra, é o mais utilizado. Neste trabalho faremos uma abordagem geral dos modelos não-lineares da família exponencial. Será introduzida a teoria da família exponencial sendo apresentada a função de densidade de probabilidade, função geratriz de cumulantes, função de verossimilhança, razão de verossimilhança e desvio do modelo; tais resultados apresentados facilitarão e/ou serão necessários na compreensão do que será feito para os modelos não-lineares da família exponencial. Será definido o modelo não-linear da família exponencial sendo apresentadas as suposições do modelo, sua função de verossimilhança e algoritmo da estimação dos parâmetros. Faremos a abordagem da análise de diagnóstico e de influência dos modelos não-lineares da família exponencial. Por fim, faremos aplicações e mostraremos a eficiência e importância na utilização desta classe, uma vez que diversos fenômenos apresentam comportamento não-linear.

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.

[pt] Esta tese apresenta uma nova classe de modelos não lineares inspirada no modelo ARN, apresentado por Mellem, 1997. Os modelos definidos nesta classe são aditivos com coeficientes variáveis modelados por redes neurais e, tanto a média quanto a variância condicionais, são modeladas explicitamente. Neste trabalho podem ser identificadas quatro partes principais: um estudo sobre os modelos mais comuns encontrados na literatura de séries temporais; um estudo sobre redes neurais, focalizando a rede backpropagation; a definição do modelo proposto e os métodos utilizados na estimação dos parâmetros e o estudo de casos. Modelos aditivos têm sido escolha preferencial na modelagem não linear: paramétrica ou não paramétrica, de média ou de variância condicional. Além disso, tanto a idéia de modelos de coeficientes variáveis quanto a de modelos híbridos. que reúnem paradigmas diferentes, não é novidade. Por esta razão, foi traçado um panorama dos modelos não lineares mais encontrados na literatura de séries temporais, focalizando-se naqueles que tinham relacionamento mais estreito com a classe de modelos proposta neste trabalho. No estudo sobre redes neurais, além da apresentação de seus conceitos básicos, analisou- se a rede backpropagation, ponto de partida para a modelagem dos coeficientes variáveis. Esta escolha deveu- se à constatação da predominância e constância no uso desta rede, ou de suas variantes, nos estudos e aplicações em séries temporais. Demonstrou-se que os modelos propostos são aproximadores universais e podem ser utilizados para modelar a variância condicional de uma série temporal. Foram desenvolvidos algoritmos, a partir dos métodos de mínimos quadrados e de máxima verossimilhança, para a estimação dos pesos, através da adaptação do algoritmo de backpropagation à esta nova classe de modelos. Embora tenham sido sugeridos outros algoritmos de otimização, este mostrou-se suficientemente apropriado para os casos testados neste trabalho. O estudo de casos foi dividido em duas partes: testes com séries sintéticas e testes com séries reais. Estas últimas, normalmente, utilizadas como benchmarking por analistas de séries temporais não lineares. Para auxiliar na identificação das variáveis do modelo, foram utilizadas regressões de lag não paramétricas. Os resultados obtidos foram comparados com outras modelagens e foram superiores ou, no mínimo, equivalentes. Além disso, é mostrado que o modelo híbrido proposto engloba vários destes outros modelos. / [en] A class of nonlinear additive varyng coefficient models is introduced in this thesis, inspired by ARN model, presented by Mellem, 1997. the coefficients are explicitly modelled. This work is divided in four major parts: a study of most common models in the time series literature; a study of neural networks, focused in backpropagation network; the presentation of the proposed models and the methods used for parameter estimation: and the case studies. Additive models has been the preferencial choice in nonlinear modelling: idea of varyng coefficient and of hybrid models, aren`t news. Hence, the models in the time series literature were analysed, assentialy those closely related with the class of models proposed in this work. Sinse the predominance and constancy in the use of backpropagation network, or its variants, in time series studies and applications, was confirmed by this work, this network was analyzed with more details. This work demonstrated that the proposed models are universal aproximators and could model explicity conditional variance. Moreover, gradient calculus and algorithms for the weight estimation were developed based on the main estimation methods: least mean squares and maximum likelihood. Even though other gradient calculus and otimization algorithms have been sugested, this one was sufficiently adequate for the studied cases. The case studies were divided in two parts: tests with synthetic series and for the nonlinear time series analysts. The obtained results were compared with other models and were superior or, at least, equivalent. Also, these results confirmed that the proposed hybrid model encompass several of the others models

Cette thèse porte sur l'identification et l'estimation des ruptures structurelles pouvant affecter des données économiques et financières à mémoire longue. Notre étude s'est limitée dans les trois premiers chapitres au cadre univarié où nous avons modélisé la dépendance de long terme et les changements structurels simultanément et séparément au niveau de la moyenne ainsi que la volatilité. Dans un premier temps nous n'avons tenu compte que des sauts instantanés d'état ensuite nous nous sommes intéressés à la possibilité d'avoir des changements graduels et lisses au cours du temps grâce à des modèles nonlinéaires plus complexes. Par ailleurs, des expériences de simulation ont été menées dans le but d'offrir une analyse comparative des méthodes utilisées et d'attester de la robustesse des tests sous certaines conditions telle que la présence de la mémoire longue dans la série. Ce travail s'est achevé sur une extension aux modèles multivariés.Ces modèles permettent de rendre compte des mécanismes de propagation d'une variation d'une série sur l'autre et d'identifier les liens entre les variables ainsi que la nature des ces liens. Les interactions entre les différentes variables financières ont été analysées tant à court terme qu'à long terme. Bien que le concept du changement structurel n'a pas été abordé dans ce dernier chapitre, nous avons pris en compte l'effet d'asymétrie et de mémoire longue dans la modélisation de la volatilité. / This dissertation deals with the detection and the estimation of structural changes in long memory economic and financial time series. Within the rest three chapters we focused on the univariate case to model both the long range dependence and structural changes in the mean and the volatility of the examined series. In the beginning we just take into account abrupt regime switches but after we use more developed nonlinear models in order to capture the smooth time variations of the dynamics. Otherwise we analyse the efficiency of various techniques permitting to select the number of breaks and we assess the robustness of the used tests in a long memory environment via simulations. Last, this thesis was completed by an extension to multivariate models. These models allow us to detect the impact of some series on the others and identify the relationships among them. The interdependencies between the financial variables were studied and analysed both in the short and the long range. While structural changes were not considered in the last chapter, our multivariate model takes into account asymmetry effects and the long memory behaviour in the volatility.

The objective of the present study is to investigate option pricing and forecasting problems in finance. This is achieved by developing stochastic models in the framework of classical modeling approach. In this study, by utilizing the stock price data, we examine the correctness of the existing Geometric Brownian Motion (GBM) model under standard statistical tests. By recognizing the problems, we attempted to demonstrate the development of modified linear models under different data partitioning processes with or without jumps. Empirical comparisons between the constructed and GBM models are outlined. By analyzing the residual errors, we observed the nonlinearity in the data set. In order to incorporate this nonlinearity, we further employed the classical model building approach to develop nonlinear stochastic models. Based on the nature of the problems and the knowledge of existing nonlinear models, three different nonlinear stochastic models are proposed. Furthermore, under different data partitioning processes with equal and unequal intervals, a few modified nonlinear models are developed. Again, empirical comparisons between the constructed nonlinear stochastic and GBM models in the context of three data sets are outlined. Stochastic dynamic models are also used to predict the future dynamic state of processes. This is achieved by modifying the nonlinear stochastic models from constant to time varying coefficients, and then time series models are constructed. Using these constructed time series models, the prediction and comparison problems with the existing time series models are analyzed in the context of three data sets. The study shows that the nonlinear stochastic model 2 with time varying coefficients is robust with respect different data sets. We derive the option pricing formula in the context of three nonlinear stochastic models with time varying coefficients. The option pricing formula in the frame work of hybrid systems, namely, Hybrid GBM (HGBM) and hybrid nonlinear stochastic models are also initiated. Finally, based on our initial investigation about the significance of presented nonlinear stochastic models in forecasting and option pricing problems, we propose to continue and further explore our study in the context of nonlinear stochastic hybrid modeling approach.

Title: Testing for linearity in time series Author: Martin Melicherčík Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zuzana Prášková, CSc., Department of Probability and Mathematical Statistics Abstract: In the first part of the thesis, a necessary theoretical base from time series analysis is explained, which is consequently used to formulate several tests for linearity. According to variety of approaches the theory includes wide range of knowledge from correlation and spectral analysis and introduces some basic nonlinear models. In the second part, linearity tests are described, classified and compared both theoretically and practically on simulated data from several linear and nonlinear models. At the end, some scripts and hints in R language are introduced that could be used when applying tests to real data. Keywords: linear time series, bispectrum, testing for linearity, nonlinear models