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.

近幾年來，非線性時間數列分析一直是時間數列及計量經濟學者所熱衷的研究主題之一，而非線性時間數列結構改變的研究也越來越受到重視。其中的門檻自迴歸模式，雖具有線性模式所不能配適的特性，但模式建構的問題，一直是其在發展應用上的瓶頸。本研究擬以門檻自迴歸模式建構的流程並結合遺傳演算法的最佳化搜尋技術，架構出時間數列遺傳演算法，藉此演算法則及程序，全域性地搜尋最佳的門檻自迴歸模式。 / Non-linear time series analysis is a research topic which the schalors of time series and econometrics are intent on, and the research of structure change of non-linear time series is attentive. Threshold autoregressive model (TAR model) of non-linear time series has some characters which linear model fail to fit while the problem of how to find an appropriate threshold value is still attracted many researchers attention. In this paper, we present about searching the parameters for a TAR model by genetic algorithms.

本篇論文檢驗聯準會模型在六個亞洲市場：中國大陸、印度、馬來西亞、新加坡、台灣和泰國是否成立。我們首先檢驗共整合檢定來觀察變數之間長期的關係；另外，針對線性的指標模型，我們則檢測其是否具有非線性的門檻自回歸情形。實證結果顯示，於共整合檢定下，六個國家的股票價格、股票報酬和十年期債券殖利率具有長期共整合關係；而在非線性的TAR模型配適下，其解釋能力優於線性的AR模型。 / This paper studies the Fed Model in six Asia countries, China, India, Malaysia, Singapore, Taiwan, and Thailand. We examine the cointegraiton test for the long-run relationship and build a nonlinear threshold autoregressive model (TAR) between the long -term government bond yield, the stock index and the earning s index. Our empirical results show that such a long-run relationship indeed exists for those countries. In addition, the explanatory power of TAR model is better than linear AR model.

時間序列是用來預測未來趨勢的一種重要技術，然而在實務上建構時間序列模型時，參數很難有效估計。原因可能來自於時間序列本身的模糊性質，而導致參數的不確定性使得預測結果產生極大誤差。如果將參數模糊化引進時間序列的模型中，往往過於複雜。本論文提出相對移動率為新的模糊時間序列建構方法，讓原本具有模糊性質的時間序列經由反模糊化(defuzzification)後，以點估計的方式估計起始中心點，經由適當的修正調整為較佳的中心點以及半徑，建立有效的區間時間序列。並將相對移動率引進門檻自廻規模型中，取代原有之門檻值設定，並建立區間時間序列。最後，我們使用台灣加權股價指數為例，以本論文所提出之方法進行區間預測及效率評估。 / The time series is an important technology that is used to predict future trends, however in the real world, parameter is difficult to estimate effectively when we construct a time series model due to the of the fuzzy property of the times series data. The estimated parameters in the time series will cause a big error due to the uncertainty of fuzzy data. It is too complex to introduce the fuzzy parameters into the time series model. In this thesis, we propose relative moving ratio as a new criteria in constructing procedure of an interval time series. We defuzzify a fuzzy data and use point estimation to obtain an initial center, then we adjust the center and radius making it more appropriately. The resulting center and radius is then become an interval time series that can be use to forecast an interval data. We also apply relative moving ratio in threshold autoregressive models by replacing the threshold in constructing interval time series. Finally, in empirical studies chapter, we use Taiwan weighted Stock Index as examples to evaluate the performance of the proposed two methods in building the interval time series.

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.

本文研究台灣貨幣需求結構改變，我們研究「變數」值(Piecewise in Variable)的結構轉折而非「時間」值(Piecewise in Time)，因為轉折點只是轉折區間的特例，所以本文建立一「變數模糊時間序列」(Fuzzy Time Series in Variable)模型來探討「變數的轉折區間」，相較於傳統時間序列研究方法如：時間序列模型、門檻轉折點模型與模糊時間序列模型等，本文所建立的變數模糊時間序列模型，所求取的股價轉折區間，不僅可改善對稱模型殘差項的非隨機現象，同時也改善了門檻轉折模型之轉折點股價指數太低的現象，並且有效地將轉折點變更為較一般化的轉折區間，足見本文所提出變數模糊時間序列模型在結構轉折的偵測上具有相對優勢，詳述如下： （一）、相較於對稱模型方面：變數模糊時間序列模型可避免對稱模型估計貨幣需求函數所產生的偏差，並且有效改善其殘差項具有非白噪音現象。 （二）、相較於門檻轉折模型方面：1.變數模糊時間序列模型較能有效驗證以下假說：貨幣需求的股價指數彈性在高股價區時較大，以及貨幣需求的所得彈性在高股價區時較小。2.變數模糊時間序列模型所求出的股價指數轉折區間水準值，對央行目前及未來貨幣政策較具實用性，3. 變數模糊時間序列模型再預測貨幣需求時，未如門檻轉折模型產生高估的偏誤。 （三）、相較於傳統模糊時間序列模型方面：變數模糊時間序列模型已改善傳統模糊時間序列模型的結構轉折區間太長之不合理現象。 （四）、相較於以「時間」為轉折的傳統時間序列模型方面：當貨幣需求函數的重要解釋變數在短時間持續發生較大幅度變化時，傳統時間序列模型可能無法診斷出結構轉變的缺失，本文的變數模糊時間序列模型可避免此一缺失。 （五）、在政策的應用上： 1. 中央銀行若未將資料，區分高低股價指數來分段估計貨幣需求函數，將使貨幣需求的所得彈性抑或是狹義貨幣需求的股價指數彈性的估計，產生頗大的偏誤。 2. 經建會在計算台灣地區的景氣對策信號中，其金融面指標同時包括有M1B貨幣供給的增加率與股價指數變動率，如此將造成在高股價指數下，股價指數上揚時高估了台灣地區的景氣狀況，而在股價指數下降時，則反之。 另外，由於台灣欠缺貨幣需求函數的重要解釋變數「所得」的月資料，以往文獻以工業生產指數等為替代變數以估計月貨幣需求函數，本文不僅證明這些方法的缺失，並提出「模糊距離權數法」來估計出月國內生產毛額資料，此一資料不僅可避免月工業生產指數等方法的三項缺失，而且在貨幣需求的估計上與預測上均有較佳的表現。 / Whether the ”money demand function” makes “structural change” happened or not ,that is crucial research for the monetary theory field. Therefore, many foreign and domestic papers have ever made studies on this. There have two major methods of study structural change. The first method is piecewise in time that is so popular and so many lecture study by it e.g. Juda and Scadding(1982), Shen(1999) ,Lin and Huang(1999),etc . Tsay(1989) had proposed a new methoed that is piecewise in variable . Distinct situation is suitable in using the two methods .We have two reasons to use the new method to study the structural change of Taiwan’s money demand function. First one is that Friedman(1988,Paul（1992）,Wu and Shea（1993）and Shen(1996) find the trade-volume of stock market or stock price are the important factors of money demand function. TSE is 12495 in February of 1990 and 2573 in October of 1990. TSE is changing so huge but all the Papers of piecewise in time can’t detect the structural change of Taiwan money demand. The second reason is that to detect the ” interval of financial variable” of structural change of Taiwan money demand is more benefit to the Central Bank than to detect the ” past time point” of structural change.　To detect the ” interval of financial variable” of structural change of Taiwan money demand is much convenient matters for monetary policy of Center Bank from now and future. Our research propose “fuzzy time series in variable” try to find the ” smoothing interval of financial variable” of structural change of money demand . Our method has two major benefits as follow: 1. Difference to TAR model: The TAR model find out the ” point of financial variable” of structural change. It seems metaphorically money demand function’s structural change suddenly. Our method find out the ” interval of financial variable” of structural change .It’s more reasonable that structural change of money demand function is gradually. 2. Difference to STAR model: So many STAR（Smooth Transition Autoregressive ）papers also find out the Gradual Transition Interval .For example: Terasvirta and Anderson(1992), Sarantis(1999) etc. But those lectures have the following point on why our method can improve it (a).STAR is piecewise in time. (b). STAR investigate structural change by just one variable AR process. But economists concern the structural change of variables. (c). The power of STAR to detect structural change is too weak. 3. We propose new summation average entropy formula that can improve the interval of structural change too longer.

The financial crisis of 2007/8 has triggered a profound debate about public budget finance sustainability, ever-increasing government expenditures and the efficiency of fiscal policy measures. Given this context, the following dissertation provides four contributions that analyze the long-run growth of government spending throughout economic development, discuss potential effects of fiscal policy measures on output, and provide new insights into the assessment of debt sustainability for a variety of industrialized countries. Since the breakout of the European debt crisis in 2009/2010, there has been a revival of interest in the long-term growth of government expenditures. In this context, the relationship between the size of the public sector and economic growth - often referred to as Wagner's law - has been in the focus of numerous studies, especially with regard to public policy and fiscal sustainability. Using historical data from the mid-19th century, the first chapter analyzes the validity of Wagner's law for five industrialized European countries and links the discussion to different stages of economic development. In line with Wagner's hypothesis, our findings show that the relationship between public spending and economic growth has weakened at an advanced stage of development. Furthermore, all countries under review support the notion that Wagner's law may have lost its economic relevance in recent decades. As a consequence of the 2007/8 financial crisis, there has been an increasing theoretical and empirical debate about the impact of fiscal policy measures on output. Accordingly, the Structural Vector Autoregression (SVAR) approach to estimating the fiscal multipliers developed by Blanchard and Perotti (2002) has been applied widely in the literature in recent years. In the second chapter, we point out that the fiscal multipliers derived from this approach include the predicted future path of the policy instruments as well as their dynamic interaction. We analyze a data set from the US and document that these interactions are economically and statistically significant. In a counterfactual simulation, we report fiscal multipliers that abstract from these dynamic responses. Furthermore, we use our estimates to analyze the recent fiscal stimulus of the American Recovery and Reinvestment Act (ARRA). The third chapter contributes to the existing empirical literature on fiscal multipliers by applying a five-variable SVAR approach to a uniform data set for Belgium, France, Germany, and the United Kingdom. Besides studying the effects of expenditure and tax increases on output, we additionally analyze their dynamic effects on inflation and interest rates as well as the dynamic interaction of both policy instruments. By conducting counterfactual simulations, which abstract from the dynamic response of key macroeconomic variables to the initial fiscal shocks, we study the importance of these channels for the transmission of fiscal policy on output. Overall, the results demonstrate that the effects of fiscal shocks are limited and rather different across countries. Further, it is shown that the inflation and interest rate channel are insignificant for the transmission of fiscal policy. In the field of public finances, governmental budgetary policies are among the most controversial and disputed areas of political and scientific controversy. The sustainability of public debt is often analyzed by testing stationarity conditions of government's budget deficits. The fourth chapter shows that this test can be implemented more effectively by means of an asymmetric unit root test. We argue that this approach increases the power of the test and reduces the likelihood of drawing false inferences. We illustrate this in an application to 14 countries of the European Monetary Union as well as in a Monte Carlo simulation. Distinguishing between positive and negative changes in deficits, we find consistency with the intertemporal budget constraint for more countries, i.e. lower persistence of positive changes in some countries, compared to the earlier literature.