This thesis is mainly concerned with the estimation of parameters of a first-order Smooth Threshold Autoregressive (STAR) model with delay parameter one. The estimation procedures include classical and Bayesian methods from a parametric and a semiparametric point of view.As the theoretical importance of stationarity is a primary concern in estimation of time series models, we begin the thesis with a thorough investigation of necessary or sufficient conditions for ergodicity of a first-order STAR process followed by the necessary and sufficient conditions for recurrence and classification for null-recurrence and transience.The estimation procedure is started by using Bayesian analysis which derives posterior distributions of parameters with a noninformative prior for the STAR models of order p. The predictive performance of the STAR models using the exact one-step-ahead predictions along with an approximation to multi-step-ahead predictive density are considered. The theoretical results are then illustrated by simulated data sets and the well- known Canadian lynx data set.The parameter estimation obtained by conditional least squares, maximum likelihood, M-estimator and estimating functions are reviewed together with their asymptotic properties and presented under the classical and parametric approaches. These estimators are then used as preliminary estimators for obtaining adaptive estimates in a semiparametric setting. The adaptive estimates for a first-order STAR model with delay parameter one exist only for the class of symmetric error densities. At the end, the numerical results are presented to compare the parametric and semiparametric estimates of this model.

[pt] Durante as últimas duas décadas, as economias do mundo têm sido caracterizadas por maior estabilidade na inflação e no produto. No entanto, aumentos na instabilidade financeira vêm preocupando os bancos centrais. Sendo assim, este trabalho tem como objetivo analisar empiricamente possíveis relações entre a política monetária brasileira e variações em preços de ativos, mais especificamente taxa de câmbio nominal e índice Bovespa. Os resultados encontrados para o período amostral de janeiro/2000 a janeiro/2006 sugerem que o modelo não-linear (TAR - threshold autoregressive) ajustase melhor aos dados brasileiros em comparação com o modelo linear e trazem indícios de que variações na taxa de câmbio nominal estão associadas a movimentos na taxa Selic em períodos mais conturbados da economia brasileira, os quais geram maior volatilidade no mercado financeiro. / [en] During the past two decades, world's economies have been characterized by stability on inflation and product levels. However, increases in financial instability are becoming a reason for concern to central banks. In this sense, the aim of this study is to analyze empirically possible relations between the Brazilian monetary policy and changes on asset prices, specifically the nominal exchange rate and the Bovespa index. The results for the sample between January, 2000 and January, 2006 suggest that the non-linear model, based on a Threshold Autoregressive model, fits better into Brazilian data than the linear model and find evidence that changes on nominal exchange rates and movements on Selic rate are associated during difficult times of the Brazilian economy, which are related to higher financial volatility.

Submitted by Winston Chun (winston.chun@gmail.com) on 2011-09-08T04:15:02Z No. of bitstreams: 1 Dissertacao VFINAL.pdf: 252650 bytes, checksum: 8b08b5f955a557fe1c18b78a33d10bda (MD5) / Rejected by Gisele Isaura Hannickel (gisele.hannickel@fgv.br), reason: Prezado Winston, O trabalho postado está com as folhas invertidas, deve seguir a seguinte sequencia: 1 - capa 2 - contra-capa 3 - ficha catalográfica 4 - folha de assinaturas. Em caso de dúvidas, favor acessar o caminho: http://bibliotecadigital.fgv.br/site/bkab/normalizacao Att, Gisele Hannickel Secretaria de Registro on 2011-09-08T12:44:39Z (GMT) / Submitted by Winston Chun (winston.chun@gmail.com) on 2011-09-08T13:30:24Z No. of bitstreams: 1 Dissertacao VFINAL.pdf: 209740 bytes, checksum: 9b370c58031ba9a9ecb5718b05d9ee82 (MD5) / Approved for entry into archive by Gisele Isaura Hannickel (gisele.hannickel@fgv.br) on 2011-09-08T13:43:33Z (GMT) No. of bitstreams: 1 Dissertacao VFINAL.pdf: 209740 bytes, checksum: 9b370c58031ba9a9ecb5718b05d9ee82 (MD5) / Approved for entry into archive by Gisele Isaura Hannickel (gisele.hannickel@fgv.br) on 2011-09-08T13:43:46Z (GMT) No. of bitstreams: 1 Dissertacao VFINAL.pdf: 209740 bytes, checksum: 9b370c58031ba9a9ecb5718b05d9ee82 (MD5) / Made available in DSpace on 2011-09-08T13:44:03Z (GMT). No. of bitstreams: 1 Dissertacao VFINAL.pdf: 209740 bytes, checksum: 9b370c58031ba9a9ecb5718b05d9ee82 (MD5) Previous issue date: 2011-08-08 / Esta dissertação tem com objetivo avaliar uma das implicações da hipótese de expectativas para a estrutura a termo de taxa de juros brasileira. Utilizando testes lineares tradicionais e através da reprodução de testes não lineares TAR de Enders e Granger (1998) e ESTAR Kapetanios e Shin (2003) conclui-se que a hipótese de expectativas não é totalmente válida para a ETTJ do Brasil, além disso, são encontradas evidências de não linearidade nas séries de spreads que demandam mais pesquisa sobre o assunto. / This dissertation has the aim to evaluate one of the implications of expectation hypothesis in Brazilian term structure of interests. Using traditional linear tests and through the reproduction of nonlinear Threshold Autoregressive (TAR) tests of Enders and Granger (1998) and Exponential Smooth Transition Autoregressive (ESTAR) of Kapetanios and Shin (2003) the conclusion is that expectation hypothesis is not totally valid for Brazil, besides that, some evidences of non-linearity in spreads series were found then more research is needed on the subject.

本論文主要在估計門檻式自動迴歸模型之參數的信賴區間。由線性自動迴歸 模型衍生出來的非線性自動迴歸模型中，門檻式自動迴歸模型是其中一種經常會被應用到的模型。雖然，門檻式自動迴歸模型之參數的漸近理論已經發展了許多；但是，相較於大樣本理論，有限樣本下參數的性質討論則較少。對於有限樣本的研究，Woodroofe (1989) 提出一種近似法：非常弱近似法。 Woodroofe 和 Coad (1997) 則利用此方法去架構一適性化線性模型之參數的修正信賴區間。Weng 和 Woodroofe (2006) 則將此近似法應用於線性自動迴歸模型。這個方法的應用始於定義一近似樞紐量，接著利用此方法找出近似樞紐量的近似期望值及近似變異數，並對此近似樞紐量標準化，則標準化後的樞紐量將近似於標準常態分配，因此得以架構參數的修正信賴區間。而在線性自動迴歸模型下，利用非常弱展開所導出的近似期望值及近似變異數僅會與一階動差及二階動差的微分有關。因此，本論文的研究目的就是在樣本數為適當的情況下，將線性自動迴歸模型的結果運用於門檻式自動迴歸模型。由於大部分門檻式自動迴歸模型的動差並無明確之形式；因此，本研究採用蒙地卡羅法及插分法去近似其動差及微分。最後，以第一階門檻式自動迴歸模型去配適美國的國內生產總值資料。 / Threshold autoregressive (TAR) models are popular nonlinear extension of the linear autoregressive (AR) models. Though many have developed the asymptotic theory for parameter estimates in the TAR models, there have been less studies about the finite sample properties. Woodroofe (1989) and Woodroofe and Coad (1997) developed a very weak approximation and used it to construct corrected confidence sets for parameters in an adaptive linear model. This approximation was further developed by Woodroofe and Coad (1999) and Weng and Woodroofe (2006), who derived the corrected confidence sets for parameters in the AR(p) models and other adaptive models. This approach starts with an approximate pivot, and employs the very weak expansions to determine the mean and variance corrections of the pivot. Then, the renormalized pivot is used to form corrected confidence sets. The correction terms have simple forms, and for AR(p) models it involves only the first two moments of the process and the derivatives of these moments. However, for TAR models the analytic forms for moments are known only in some cases when the autoregression function has special structures. The goal of this research is to extend the very weak method to the TAR models to form corrected confidence sets when sample size is moderate. We propose using the difference quotient method and Monte Carlo simulations to approximate the derivatives. Some simulation studies are provided to assess the accuracy of the method. Then, we apply the approach to a real U.S. GDP data.