The purpose of this thesis is to study a restricted multivariate AFRMA model, called the Homogeneous Model. This model is defined as one in which each univariate component of the multivariate model is of the same order in p and q as it is in the multivariate model. From a mathematical respect, multivariate ARMA model is homogeneous if , and only if, its coefficient matrices are diagonal. From a physical respect, the present observation of a phenomenon can be modeled only by it s own past observation and its present and past "errors." The estimation procedures are developed based on maximum likelihood method and on O'Connell' s method for univariate model. The homogeneous model is evaluated by four types of data. Those data are generated reflecting different degrees of nonhomogeneity. It is found that the homogeneous model is sensitive to departures from the homogeneous assumptions. Small departures cause no serious problem, however, large departures are serious.

The family of stable distributions represents an important generalization of the Gaussian family; stable random variables obey a generalized central limit theorem where the assumption of finite variance is replaced with one of power law decay in the tails. Possessing heavy tails, asymmetry, and infinite variance, non-Gaussian stable distributions can be suitable for inference in settings featuring impulsive, possibly skewed noise. A general lack of analytical form for the densities and distributions of stable laws has prompted research into computational methods of estimation. This report introduces stable distributions through a discussion of their basic properties and definitions in chapter 1. Chapter 2 surveys applications, and chapter 3 discusses a number of procedures for inference, with particular attention to time series models in the ARMA setting. Further details and an application can be found in the appendices. / text

This thesis deals with the financial time series model identification. The univariate and multivariate ARMA models and their identification criteria are described. The procedures using the correlation structure of the time series and some information criteria are presented. The functioning of the criteria is verified on simulated time series AR, MA and ARMA. Afterwards, the criteria are compared in terms of reliability and simplicity of use. Finally, there are two examples of univariate and multivariate ARMA model identification for the real financial time series. The data and the R programme source code are enclosed on a CD. Powered by TCPDF (www.tcpdf.org)

Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This work presents the GARMA model with discrete distributions and application of resampling techniques to this class of models. We also proposed The Bayesian approach on GARMA models. The TGARMA (Transformed Generalized Autoregressive Moving Average) models was proposed, using the Box-Cox power transformation. Last but not least we proposed the Bayesian approach for the TGARMA (Transformed Generalized Autoregressive Moving Average). / Modelos Autoregressivos e de médias móveis generalizados (GARMA) são uma classe de modelos que foi desenvolvida para extender os conhecidos modelos ARMA com distribuição Gaussiana para um cenário de series temporais não Gaussianas. Este trabalho apresenta os modelos GARMA aplicados a distribuições discretas, e alguns métodos de reamostragem aplicados neste contexto. É proposto neste trabalho uma abordagem Bayesiana para os modelos GARMA. O trabalho da continuidade apresentando os modelos GARMA transformados, utilizando a transformação de Box-Cox. E por último porém não menos importante uma abordagem Bayesiana para os modelos GARMA transformados.

Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This work presents the GARMA model with discrete distributions and application of resampling techniques to this class of models. We also proposed The Bayesian approach on GARMA models. The TGARMA (Transformed Generalized Autoregressive Moving Average) models was proposed, using the Box-Cox power transformation. Last but not least we proposed the Bayesian approach for the TGARMA (Transformed Generalized Autoregressive Moving Average). / Modelos Autoregressivos e de médias móveis generalizados (GARMA) são uma classe de modelos que foi desenvolvida para extender os conhecidos modelos ARMA com distribuição Gaussiana para um cenário de series temporais não Gaussianas. Este trabalho apresenta os modelos GARMA aplicados a distribuições discretas, e alguns métodos de reamostragem aplicados neste contexto. É proposto neste trabalho uma abordagem Bayesiana para os modelos GARMA. O trabalho da continuidade apresentando os modelos GARMA transformados, utilizando a transformação de Box-Cox. E por último porém não menos importante uma abordagem Bayesiana para os modelos GARMA transformados.

This thesis deals with analyzing multivariate financial and economical data. The first section describes the theory of multivariate time series and multivariate ARMA models. The second part deals with some models with exogenous variables such as simultaneous equations models and ARMAX model. In the final chapter, the described theory is applied to analyze the reciprocal dependence of time series of inflation rates and dependence of inflation rates on various macroeconomical indicators. The results were obtained by software Mathematica 8, Mathematica 10, EViews and R. Powered by TCPDF (www.tcpdf.org)

In this work, the random vibration of higher-order nonlinear beams and composite plates subjected to stochastic loading is studied. The fourth-order nonlinear beam equation is examined to study the effect of rotary inertia and shear deformation on the root mean square values of displacement response. A new linearly coupled equivalent linearization method is proposed and compared with the widely used traditional equivalent linearization method. The new method is proven to yield closer predictions to the numerical simulation results of the nonlinear beam vibration. A systematical investigation of the nonlinear random vibration of composite plates is conducted in which effects of nonlinearity, choices of different plate theories (the first order shear deformation plate theory and the classical plate theory), and temperature gradient on the plate statistical transverse response are addressed. Attention is paid to calculate the R.M.S. values of stress components since they directly affect the fatigue life of the structure. A statistical data reconstruction technique named ARMA modeling and its applications in random vibration data analysis are discussed. The model is applied to the simulation data of nonlinear beams. It is shown that good estimations of both the nonlinear frequencies and the power spectral densities are given by the technique. / Ph. D.

nÃo hà / A sonegaÃÃo fiscal à um problema para o Estado equilibrar suas contas e manter a mÃquina pÃblica exercendo seu papel social plenamente. O ICMS representa quase a totalidade da arrecadaÃÃo tributÃria do Estado. Entretanto, os contribuintes buscam meios de diminuir o peso da carga tributÃria por meio de elisÃo e sonegaÃÃo fiscal. Assim, este trabalho busca analisar o quanto o Estado consegue reaver dos seus crÃditos tributÃrios que sÃo provenientes de sonegaÃÃo do ICMS. A metodologia utilizada para a anÃlise do problema foi a de Box e Jenkins para prever a sÃrie temporal do total de crÃditos que foram transformados em receita para o Estado para os dados dos setores de Alimentos, Automotivos, Bebidas, CombustÃveis, ComunicaÃÃo, Couros e CalÃados, Energia, FarmacÃuticos, QuÃmicos, TÃxtil e Total nos meses de janeiro de 2006 a dezembro de 2011, realizados pela Auditoria Fiscal da SEFAZ-CE. / The tax evasion is a problem for the state balance its accounts public and maintain the machine fully exercising their social role. The ICMS represents almost all of the tax revenue of the State. However, taxpayers looking for ways to lighten the tax burden through tax avoidance and tax evasion. This study aims to analyze how the state can regain its tax credits that come from evasion of ICMS. The methodology used for the analysis of the problem was the Box-Jenkins time series to predict the total number of credits that have been turned into revenue for the state data for the sectors of Food, Automotive, Beverage, Fuel, Communication, Leather and Footwear, Energy, Pharmaceuticals, Chemicals, Textiles and Total from January 2006 to December 2011, conducted by the Comptroller SEFAZ-CE

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-10-06T18:14:46Z No. of bitstreams: 1 TeseEAMms.pdf: 1490434 bytes, checksum: e7a807666b453630ffb423774d2539b9 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T13:51:46Z (GMT) No. of bitstreams: 1 TeseEAMms.pdf: 1490434 bytes, checksum: e7a807666b453630ffb423774d2539b9 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T13:51:52Z (GMT) No. of bitstreams: 1 TeseEAMms.pdf: 1490434 bytes, checksum: e7a807666b453630ffb423774d2539b9 (MD5) / Made available in DSpace on 2016-10-20T13:52:00Z (GMT). No. of bitstreams: 1 TeseEAMms.pdf: 1490434 bytes, checksum: e7a807666b453630ffb423774d2539b9 (MD5) Previous issue date: 2016-03-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / From the generalized normal distribution and concepts of the generalized autoregressive moving averages models we introduce the generalized normal-ARMA model as an alternative way to model time series exhibiting symmetry and tails that may be lighter or heavier when compared the normal distribution. We present application for proposed model using three time series in the hydrology, economy and publics policy areas. The proposed model is presented as good alternative when compared to ARMA model with normal distribution. We extended this model the case of the asymmetric time series. In this case we used the Box-Cox transformation, denoted by Box-Cox generalized normal ARMA. The particular case, when we use the logarithmic transformation is called generalized log-normal ARMA. We adjusted the models with transformation to the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants. We obtain the prediction values for the model with transformation, that are better when compared with the model without transformation. To treat time series that exhibit periodic in the correlation function we defined three extensions for periodic autoregressive model, called generalized normal periodic autoregressive model, generalized log-normal periodic autoregressive model and Box-Cox generalized normal periodic autoregressive model. We can observed that the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants have periodic correlation. We present two applications of periodic models from these series. In the models, we note that is not necessary the use of generalized normal distribution in every months, just in some the generalized normal distribution presented better results than the normal distribution. Finally, we define the generalized normal zero inflated distribution and the generalized normal zero inflated ARMA model for time series. Adopting the model for series that have zero inflation and the maximum likelihood method for estimation of parameters, we analyze the serie of the amount of rainfall in the city of São Carlos. / A partir da distribuição normal generalizada e dos conceitos do modelo autorregressivo e de médias móveis generalizado, introduzimos o modelo normal generalizada- ARMA, como alternativa para modelar séries temporais, que exibem simetria e caudas mais leves ou mais pesadas quando comparadas com a distribuição normal. Apresentamos aplicações do modelo proposto, usando três séries temporais, das áreas de hidrologia, políticas públicas e economia. O modelo proposto se apresentou como uma boa alternativa ao modelo ARMA com distribuição normal. Estendemos o modelo para o caso de séries que apresentam assimetria. Neste caso, utilizamos a transformação de Box-Cox, denotado por Box-Cox normal generalizada-ARMA. O caso particular quando utilizamos a transformação logarítmica é chamado de log-normal generalizada-ARMA. Ajustamos os modelos com transformação à séries de vazões das usinas hidrelétricas de Furnas e Sobradinho. Calculamos predições, que para o modelo com transformação, foram melhores, quando comparado ao modelo sem transformação. Com o objetivo de tratar séries que apresentam periodicidade na função de correlação, definimos três extensões do modelo autorregressivo periódico, chamando-os de modelo normal generalizada autorregressivo periódico, modelo log-normal generalizada autorregressivo periódico e modelo Box-Cox normal generalizada autorregressivo periódico. Constatamos que as séries de vazões das usinas hidrelétricas de Furnas e Sobradinho apresentam correlação periódica. Apresentamos duas aplicações dos modelos periódicos propostos usando estas séries. Nos ajustes dos modelos, notamos que não há necessidade da utilização da distribuição normal generalizada em todos os meses, mas em alguns a distribuição normal generalizada se sobressaiu em relação a distribuição normal. Por último, definimos a distribuição normal generalizada zero inflacionada e o modelo para séries temporais normal generalizada zero inflacionada-ARMA. Adotando o método de máxima verossimilhança e o modelo para séries que apresentam inflação de zeros, analisamos a série da quantidade de precipitação pluviométrica da cidade de São Carlos.

O objetivo deste trabalho é propor os modelos Zero Modificados com distribuição na família Série de Potência (ZMPS) para séries temporais com dados de contagem. O modelo ZMPS possui um amplo portfólio de distribuições para dados de contagem em que, com uma função de ligação apropriada, podemos escrever os modelos de regressão usando as distribuições ZMPS de forma semelhante ao que é feito com os modelos lineares generalizados. Em seguida, utilizamos a ideia dos modelos Generalizados Autorregressivos e de Médias Móveis (GARMA) para finalmente propor os modelos Série de Potência Zero-Modificado para Séries Temporais com dados de contagem. / The goal of this work is to propose the Zero-Modified models with Power Series distribution (ZMPS) for time series with counting data. The ZMPS model have a huge portfolio of count data distributions wherein, with an appropriate link function, we can write the regression models using the ZMPS distributions similar to what is done with generalized linear models. Then, we can use the idea of the Generalized Autoregressive and Moving Average (GARMA) models to propose the Zero-Modified Power Series models for Time Series with counting data.