Econometric and predictive modeling techniques are two popular forecasting techniques. Both ofthese techniques have their own advantages and disadvantages. In this thesis some econometricmodels are considered and compared to predictive models using sales data for five products fromICA a Swedish retail wholesaler. The econometric models considered are regression model,exponential smoothing, and ARIMA model. The predictive models considered are artificialneural network (ANN) and ensemble of neural networks. Evaluation metrics used for thecomparison are: MAPE, WMAPE, MAE, RMSE, and linear correlation. The result of this thesisshows that artificial neural network is more accurate in forecasting sales of product. But it doesnot differ too much from linear regression in terms of accuracy. Therefore the linear regressionmodel which has the advantage of being comprehensible can be used as an alternative to artificialneural network. The results also show that the use of several metrics contribute in evaluatingmodels for forecasting sales. / Program: Magisterutbildning i informatik

Title: Exponential control of homogeneous Markov processes Author: Pavol Stanek Department: Department of Probability and Mathematical Statistics, MFF UK Supervisor: Mgr. Peter Dostál Ph.D., Department of Probability and Mathematical Statistics, MFF UK Abstract: This master thesis concerns exponential control of Markov decision chains. An iterative alghorithm for finding a control, that maximizes a long term growth rate of expected utility is developed. The utility is measured by exponential utility function. The algorithm is derived for both discrete time and continuous time chain. Subsequently, the results are applied on the problem of optimally managing port- folio with proportional transaction costs. The dynamics of the investor's position is derived and the consequent process is approximated by Markov chain. Using the iterative alghorithm, the optimal trading strategy is numerically found. Keywords: exponential control, Markov chain, portfolio optimization, proportional transaction costs 1

O objetivo deste trabalho é comparar as estruturas de vizinhanças espaciais ou matrizes de pesos espaciais da classe de modelos autorregressivos e de médias móveis espaço-temporais (STARMA). O modelo STARMA é empregado para descrever dados de séries temporais espacialmente localizados, ele é caracterizado pela dependência linear defasada tanto no espaço quanto no tempo. Foram realizadas simulações utilizando vários modelos de covariância espaço-temporal para comparar diferentes estruturas de construção da matriz de pesos espaciais com a finalidade de identificar a melhor matriz. As matrizes espaciais com pesos exponenciais apresentaram os melhores desempenhos de ajuste dos modelos STAR; e mostram uma estabilidade em relação à medida de ajuste. Por fim para ilustração, será ajustado um modelo STARMA para um conjunto de dados mensais do índice FIPEZAP de preço imobiliário de venda para apartamentos de dois dormitórios de seis cidades metropolitanas de São Paulo. / The objective of this work is to compare spatial neighborhoods structures, or the same as spatial weights matrices of the class of space-time autoregressive and moving average models STARMA. The STARMA model is used to describe spatially localized time series datas, it is characterized by the linear dependence lagged both in space and time. Simulations were performed using several space-time covariance models to compare different structures of construction of the weight matrix with the purpose of identifying the best matrix. The spatial matrices with exponential weights presented the best adjustment performances of the STAR models ans showed a stability in relation to the adjustment measure. Finally, for illustration, a STARMA model will be adjusted for a set of monthly data of the FIPEZAP real estate price index for two bedroom apartments in six metropolitan cities of São Paulo.

Made available in DSpace on 2016-04-27T16:58:53Z (GMT). No. of bitstreams: 1 Alexandra Garrote Angiolin.pdf: 2099847 bytes, checksum: eb474a043e9031508589dab1e1132ccf (MD5) Previous issue date: 2009-05-20 / Secretaria da Educação do Estado de São Paulo / This study has the objectives of investigating how to make constructivist perspectives of learning compatible with the planning the teaching-learning process, in the particular case of exponential functions and analyzing the performance of teachers of Mathematics with regard to the activities of the planning and development of teaching, in a way compatible with a constructivist perspective of learning. It is based on the work of Simon (1995) on hypothetical learning trajectories (HLTs). This is qualitative research involving two teachers of Mathematics from a state public school in Sao Paulo and their work with 77 students in the first year of Junior High School. We produced a hypothetical learning trajectory based on specific objectives and, taking as our reference hypotheses on student learning, we sought to propose tasks that involve the resolution of problems, investigation, the use of technologies, interdisciplinary approaches, applications to everyday situations and in other areas of knowledge. The HLT was implemented by the participating teachers in their own classes. From the analysis of the data obtained, we realized the complexity of producing proposals with the purpose of allowing students to build upon their own knowledge on the subject. In the same way, we experienced the challenge of facing teachers in developing tasks in this constructivist perspective, even when the intentions had been discussed and decided together. The teacher has a decisive role as, even when the teaching is planned within a constructivist perspective, what will really make this happen depends upon how he puts it into practice in the classroom. With regard to the students, when he is involved with less usual tasks that involve the reading of texts or the use of a computer, investigations show that these possibilities are promising in the sense of what occurs in learning, but various factors, which include the performance of the teacher himself, do not allow one to formulate more confident assertions upon these proposals / O presente trabalho tem como objetivo investigar como compatibilizar perspectivas construtivistas de aprendizagem com a planificação de ensino, no caso particular de funções exponenciais. Pretende-se ainda analisar a atuação dos professores de Matemática, no que se refere às atividades de planejamento e desenvolvimento de ensino, de forma compatível com uma perspectiva construtivista de aprendizagem. Como fundamentação teórica, recorremos nessa obra aos trabalhos de Simon (1995) sobre trajetórias hipotéticas de aprendizagem (THA). Trata-se de uma pesquisa qualitativa, envolvendo dois professores de Matemática, de uma escola pública estadual de São Paulo e suas atuações junto a 77 alunos da 1ª Série do Ensino Médio. Elaboramos uma trajetória hipotética de aprendizagem a partir de objetivos específicos e, tendo como referência hipóteses sobre a aprendizagem dos estudantes, buscando a proposição de tarefas que envolvessem resolução de problemas, investigação, uso de tecnologias, abordagens interdisciplinares e aplicações em situações do cotidiano e em outras áreas de conhecimento. A THA foi aplicada pelos professores participantes com, suas respectivas turmas. Com a análise dos dados obtidos, constatamos a complexidade de elaboração de propostas com a finalidade de que os alunos possam construir seus próprios conhecimentos sobre o assunto. Da mesma forma, vivenciamos o desafio a ser enfrentado pelos professores em desenvolver tarefas nessa perspectiva construtivistas, mesmo quando as intenções tenham sido discutidas e compartilhadas. O professor tem papel decisivo, pois mesmo que o ensino seja planificado numa perspectiva construtivista, o que realmente fará com que isso ocorra depende de como ele a desenvolve em sala de aula. Com relação aos alunos, seu envolvimento com tarefas menos usuais que envolviam leitura de textos, uso do computador, investigações mostraram que essas possibilidades são promissoras no sentido de que ocorra a aprendizagem, mas diversos fatores, dentre os quais a própria atuação do professor, não permitem que se formule assertivas mais contundentes sobre essas propostas

[pt] Esta dissertação tem como objetivo principal a proposição de modelos para previsão, em um curto prazo, do número de processos que são ajuizados em desfavor de uma empresa do setor elétrico. A metodologia utilizada consiste em, a partir de uma análise exploratória dos dados, construir modelos usando uma estratégia bottom-up, ou seja, parte-se de um modelo simples e processa-se seu refinamento até encontrar um modelo apropriado que mais se adeque à realidade. Partiu-se então de um modelo auto projetivo indo até uma formulação de um modelo de regressão dinâmica. Os modelos são então comparados segundo alguns critérios, basicamente no que tange à sua eficiência preditiva. Conclui-se ao final sobre a eficiência de se utilizar modelos de regressão dinâmica para este tipo de previsão tendo em vista a presença de correlação serial dos resíduos, comumente presentes nas séries econômicas. Propõe-se, ao final, uma ferramenta para, a partir dos valores estimados, analisar a viabilidade econômica de estimular ou desestimular as medidas responsáveis pela geração de processos contra a empresa. / [en] The aim of this dissertation is to develop short term models to forecast the number of judicial process in electric sector companies. From the methodology point of view, data is analyzed and models using bottom-up strategy is developed. In other words, a simple model is improved step by step until a proper model that fits well the reality is found. From a univariate model it ends up in a dynamic regression model. The models obtained in this study are compared according to some criterion, mainly forecast accuracy. In the end the conclusion is about the efficiency of dynamic regression models for this kind of forecast, which one presents data with serial correlation of residues, commonly present in economic series. In the end, from the estimated values, it´s proposed a mechanism to analyze the economic viability, to encourage or not, actions which are responsible for instigating judicial processes against the company.

在本文中，我們證明了：若對應於壽命分佈函數F之更新函數為凸（ 凹 ）族，因此解決了Shaked和Zhu(1992)所提出的兩個問題。 蝻う漫宒銵A 我們進一步得到了於某些特定之壽命分佈函數族中， / We prove that if the renewal function M(t) corresponding to a life distribution F is convex(resp. concave) then F is NBU(resp. NWU), and hence answer two questions posed by Shaked and Zhu(1992). Moreover, based on the renewal function, some characterizations of the exponential distribution within certain classes of life distributions are given. Key words and phrases:exponential distribution;renewal counting process; DFR;NBU;NWU;NBUE;NWUE.

<p>This thesis deals with a model of nonlinearly perturbed continuous-time renewal equation with nonpolynomial perturbations. The characteristics, namely the defect and moments, of the distribution function generating the renewal equation are assumed to have expansions with respect to a non-polynomial asymptotic scale: $\{\varphi_{\nn} (\varepsilon) =\varepsilon^{\nn \cdot \w}, \nn \in \mathbf{N}_0^k\}$  as $\varepsilon \to 0$, where $\mathbf{N}_0$ is the set of non-negative integers, $\mathbf{N}_0^k \equiv \mathbf{N}_0 \times \cdots \times \mathbf{N}_0, 1\leq k <\infty$ with the product being taken $k$ times and $\w$ is a $k$ dimensional parameter vector that satisfies certain properties. For the one-dimensional case, i.e., $k=1$, this model reduces to the model of nonlinearly perturbed renewal equation with polynomial perturbations which is well studied in the literature.  The goal of the present study is to obtain the exponential asymptotics for the solution to the perturbed renewal equation in the form of exponential asymptotic expansions and present possible applications.</p><p>The thesis is based on three papers which study successively the model stated above. Paper A investigates the two-dimensional case, i.e. where $k=2$. The corresponding asymptotic exponential expansion for the solution to the perturbed renewal equation is given. The asymptotic results are applied to an example of the perturbed risk process, which leads to diffusion approximation type asymptotics for the ruin probability.  Numerical experimental studies on this example of perturbed risk process are conducted in paper B, where Monte Carlo simulation are used to study the accuracy and properties of the asymptotic formulas. Paper C presents the asymptotic results for the more general case where the dimension $k$ satisfies $1\leq k <\infty$, which are applied to the asymptotic analysis of the ruin probability in an example of perturbed risk processes with this general type of non-polynomial perturbations.  All the proofs of the theorems stated in paper C are collected in its supplement: paper D.</p>

<p>The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying</p><p>asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.</p>

This thesis presents Bayesian solutions to inference problems for three types of social network data structures: a single observation of a social network, repeated observations on the same social network, and repeated observations on a social network developing through time. A social network is conceived as being a structure consisting of actors and their social interaction with each other. A common conceptualisation of social networks is to let the actors be represented by nodes in a graph with edges between pairs of nodes that are relationally tied to each other according to some definition. Statistical analysis of social networks is to a large extent concerned with modelling of these relational ties, which lends itself to empirical evaluation. The first paper deals with a family of statistical models for social networks called exponential random graphs that takes various structural features of the network into account. In general, the likelihood functions of exponential random graphs are only known up to a constant of proportionality. A procedure for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods is presented. The algorithm consists of two basic steps, one in which an ordinary Metropolis-Hastings up-dating step is used, and another in which an importance sampling scheme is used to calculate the acceptance probability of the Metropolis-Hastings step. In paper number two a method for modelling reports given by actors (or other informants) on their social interaction with others is investigated in a Bayesian framework. The model contains two basic ingredients: the unknown network structure and functions that link this unknown network structure to the reports given by the actors. These functions take the form of probit link functions. An intrinsic problem is that the model is not identified, meaning that there are combinations of values on the unknown structure and the parameters in the probit link functions that are observationally equivalent. Instead of using restrictions for achieving identification, it is proposed that the different observationally equivalent combinations of parameters and unknown structure be investigated a posteriori. Estimation of parameters is carried out using Gibbs sampling with a switching devise that enables transitions between posterior modal regions. The main goal of the procedures is to provide tools for comparisons of different model specifications. Papers 3 and 4, propose Bayesian methods for longitudinal social networks. The premise of the models investigated is that overall change in social networks occurs as a consequence of sequences of incremental changes. Models for the evolution of social networks using continuos-time Markov chains are meant to capture these dynamics. Paper 3 presents an MCMC algorithm for exploring the posteriors of parameters for such Markov chains. More specifically, the unobserved evolution of the network in-between observations is explicitly modelled thereby avoiding the need to deal with explicit formulas for the transition probabilities. This enables likelihood based parameter inference in a wider class of network evolution models than has been available before. Paper 4 builds on the proposed inference procedure of Paper 3 and demonstrates how to perform model selection for a class of network evolution models.

The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.