The emphasis of this diploma thesis is placed on the verification of stationarity in time series using the Unit Root Tests and their most common modifications that are introduced in the theoretical part of this paper. Tests mainly by Dickey and Fuller, Phillips and Perron, and KPSS test are introduced as well as their modifications in the form of ERS, Ng and Perron, and Leybourne and McCabe tests. Moreover the HEGY test for testing stationarity in the seasonal Time series and Perron test of structural breaks for Time series with shocks are described. There is also outlined the process of testing multiple Unit Roots. The empirical part of this paper consists of simulations of AR(1) time series generated using the software R, their testing for stationarity by selected Unit Root tests and the comparison of power of these tests. The conclusion includes recommendations which tests and under what conditions are the most suitable for testing Time series for the presence of Unit Root.

Panel data analysis is the modern approach of statistical and econometric modeling. The aim of the thesis is to estimate the gravity model of international trade in alcoholic beverages in the form of bilateral trade flow depending on the gross domestic product and other associated variables that facilitate trading. The data have a panel structure. Based on the results of panel unit root tests the stationarity of variables in the panel and the expected long-term relationship between the analyzed variables are tested. Gravity model is assuming the existence of long-term relationships built through various methods, such as pooling OLS estimate, fixed and random effects models, cointegrated regression DOLS and FMOLS. Cointegration relationship is verified by Pedroni panel test.

本文的主要目的在於探討亞洲國家央行外匯存底的需求，研究的國家包括韓國、大陸、印度、新加坡、台灣與日本。透過使用1987年Engle-Granger的共整合分析法，我們發現這六國的外匯存底需求與其解釋變數具有共整合的現象。共整合現象的存在反映了這些國家的外匯存底需求存在長期的均衡關係。此外，為了進一步了解短期經濟的干擾如何影響外匯存底的需求，本文採用誤差修正模型做為分析工具，與過去文獻不同的是，本文的實證結果顯示本文所研究的六個國家之外匯存底顯著的受到貨幣成長率的影響，依據誤差修正模型的調整項亦可發現當外匯存底需求偏離長期均衡值時，此六國的調整速度相當慢，絕對值都在0.5以下，由於當一個經濟體系允許以緩慢的修正速度調整至長期均衡，必須擁有大量的外匯存底，由於本文所挑選的國家為全球著名的外匯存底持有國，其央行皆持有巨額的外匯存底，故本文的實證結果與理論假設一致。 / The primary purpose of this paper is to explore the demand characteristics for international reserves in some Asian countries including Korea, China, India, Singapore, Taiwan, and Japan. After applying the cointegration test of Engle-Granger (1987), we discover that the non-stationary macro time series of the group of the countries under study are cointegrated. Hence, international reserves in these Asian countries have displayed a long-run relationship with some determinants for the past several decades. Besides, we adopt an error correcting mechanism specification to investigate the short-run dynamic process of reserve holdings. Based on the error correction model (ECM), the rate of monetary growth is found to have a significant effect on reserve holdings in all of the six countries. In the end, the properties of the error correction terms among these countries are examined. We find that the absolute value of the error correction term is less than 0.5 in these economies. It implies that all of these six countries have very low adjustment speed of the demand for reserves. Owing to the huge stock of reserve holdings in this area, the results appear to be sensible.

A literatura referente a testes de hipótese em modelos auto-regressivos que apresentam uma possível raiz unitária é bastante vasta e engloba pesquisas oriundas de diversas áreas. Nesta dissertação, inicialmente, buscou-se realizar uma revisão dos principais resultados existentes, oriundos tanto da visão clássica quanto da bayesiana de inferência. No que concerne ao ferramental clássico, o papel do movimento browniano foi apresentado de forma detalhada, buscando-se enfatizar a sua aplicabilidade na dedução de estatísticas assintóticas para a realização dos testes de hipótese relativos à presença de uma raíz unitária. Com relação à inferência bayesiana, foi inicialmente conduzido um exame detalhado do status corrente da literatura. A seguir, foi realizado um estudo comparativo em que se testa a hipótese de raiz unitária com base na probabilidade da densidade a posteriori do parâmetro do modelo, considerando as seguintes densidades a priori: Flat, Jeffreys, Normal e Beta. A inferência foi realizada com base no algoritmo Metropolis-Hastings, usando a técnica de simulação de Monte Carlo por Cadeias de Markov (MCMC). Poder, tamanho e confiança dos testes apresentados foram computados com o uso de séries simuladas. Finalmente, foi proposto um critério bayesiano de seleção de modelos, utilizando as mesmas distribuições a priori do teste de hipótese. Ambos os procedimentos foram ilustrados com aplicações empíricas à séries temporais macroeconômicas. / Testing for unit root hypothesis in non stationary autoregressive models has been a research topic disseminated along many academic areas. As a first step for approaching this issue, this dissertation includes an extensive review highlighting the main results provided by Classical and Bayesian inferences methods. Concerning Classical approach, the role of brownian motion is discussed in a very detailed way, clearly emphasizing its application for obtaining good asymptotic statistics when we are testing for the existence of a unit root in a time series. Alternatively, for Bayesian approach, a detailed discussion is also introduced in the main text. Then, exploring an empirical façade of this dissertation, we implemented a comparative study for testing unit root based on a posteriori model's parameter density probability, taking into account the following a priori densities: Flat, Jeffreys, Normal and Beta. The inference is based on the Metropolis-Hastings algorithm and on the Monte Carlo Markov Chains (MCMC) technique. Simulated time series are used for calculating size, power and confidence intervals for the developed unit root hypothesis test. Finally, we proposed a Bayesian criterion for selecting models based on the same a priori distributions used for developing the same hypothesis tests. Obviously, both procedures are empirically illustrated through application to macroeconomic time series.

O objetivo desse trabalho é analisar a influência que fundamentos internos e fatores externos exercem sobre a taxa de juros nominal dos títulos soberanos de longo prazo nos países emergentes. A base de dados engloba 13 países ao longo de 33 trimestres entre 2006 e 2014. A metodologia utilizada aborda as técnicas econométricas mais recentes para tratar dados macroeconômicos. O modelo estimado é o Pooled Mean Group desenvolvido por Pesaran, Shin e Smith (1999). O modelo consegue separar as variáveis que afetam o nível de equilíbrio da taxa de juros das que exercem efeito apenas no curto prazo. Na melhor especificação apresentada, os resultados indicam que as variáveis que causam flutuações de curto prazo na taxa de juros dos países emergentes são a taxa de juros livre de risco (+0,3), a taxa de curto prazo (+0,4) e o déficit do governo americano (+0,1). Já as variáveis que afetam o nível de equilíbrio são a taxa de juros livre de risco (+0,5), a aversão ao risco dos investidores (+0,1), o saldo em conta corrente (-0,3), a inflação (+0,1), a abertura econômica (-0,04) e a dívida bruta (efeito positivo não linear). Por fim, ao analisar exclusivamente o caso brasileiro, nosso modelo indica que se o país tivesse mantido os fundamentos internos em linha com a média dos outros emergentes desde o final de 2006, o Brasil iria chegar ao final de 2014 com uma taxa de juros nominal de longo prazo de 6,1%, 6 p.p. abaixo do valor efetivamente observado que foi de 12,1%. / The aim of this study is to analyze the influence that internal fundamentals and external factors have on long-term sovereign bond yields in emerging markets. The database covers 13 countries over 33 quarters between 2006 and 2014. The methodology addresses the latest techniques to deal with macro panels, such as panel unit root and panel cointegration tests. The estimated model is the Pooled Mean Group developed by Pesaran, Shin e Smith (1999). This model can separate the variables that affect the interest rate equilibrium from the ones that only have an effect in the short-run. In the best specification presented, the results indicates that in the short-run the variables that affects the interest rates in emerging markets are the risk free interest rate (+0.3), the short term interest rate (+0.4) and the American government deficit (+0.1). The variables that affects the equilibrium level are the risk free interest rate (+0.5), risk aversion (+0.1), current account balance (-0.3), inflation (+0.1), trade openness (-0.04) and gross debt (non-linear positive effect). Finally, by examining only the Brazilian case, our model indicates that if the country had maintained the internal fundamentals in line with the average of other emerging markets since the end of 2006, Brazil would reach the end of 2014 with a long-term interest rate of 6.1%, 6 p.p. below the actual value of 12.1%.

Made available in DSpace on 2015-03-05T18:57:20Z (GMT). No. of bitstreams: 0 Previous issue date: 9 / Nenhuma / Essa dissertação procura avaliar a dinâmica da inflação no Brasil no período de março de 2000 a dezembro de 2007, através de uma Curva de Phillips híbrida, na especificação que permite além do termo “forward looking”, representado pela expectativa de inflação, o termo “backward looking” através da inflação defasada. Inicialmente, procura-se fazer uma exposição da teoria da Curva de Phillips, partindo da abordagem clássica até a abordagem dos novos keynesianos. A revisão da literatura destaca que a Curva de Phillips tem dificuldade em se ajustar à dinâmica da inflação. Dessa forma, a inclusão do termo que representa a inércia da inflação melhora sua adequação. Conjuntamente, o nível de atividade representado pelo hiato do produto não é estatisticamente significativo, fato esse que é suportado por outros trabalhos na literatura. Avalia-se a utilização do custo unitário do trabalho como proxy do nível de atividade, e os resultados não se alteram significativamente. Os dados de inflação relativos ao último trimes / This dissertation assess the inflation dynamics in Brazil through a hybrid Phillips Curve, at the specification that allows the "forward term", represented by inflation expectation, and the "backward term" through by inertial inflation. Initially, several approaches for the Phillips Curve's theory, from classical to new Keynesian, are presented and detailed. As pointed out by the precedent literature, it is shown that the Phillips Curve has some difficulty in adjusting to the inflation dynamics and, as a consequence, that the addition of the “backward term” enhances its fit. Furthermore, the inclusion of a proxy variable for the level of activity, represented by the output gap, is not statistically significant, result supported by previous studies in literature. Finally, it is analyzed the use of a unit labor cost as a proxy for the level of activity, with no significant changes in the results. The inflation data regarding the last tree months of 2002 are influenced by the effects of the political crisis at t

New keynesian Phillips curve (NKPC) has become a central model to study the relation between inflation and real economic activity, notably in the framework of optimal monetary policy design. However, some recent evidence suggests that empirical data are usually at odds with the underlying theory. The model due to its inherent structure represents a statistical challenge in its own right. Since Galí and Gertler (1999) published their seminal paper introducing estimation via GMM techniques, they have triggered a heated debate on its empirical relevance. Their approach has been heavily criticised by later authors, mainly on the grounds of questionable behaviour of GMM estimator in the NKPC context and/or its small sample properties. The common criticism includes sensitivity to the choice of instrument set, weak identification and small sample bias. In this thesis I propose a new estimation strategy that provides a remedy to above mentioned shortcomings and allows to obtain reliable estimates. The procedure exploits recent advances in GMM theory as well as in other fields of statistics, in particular in the area of time series factor analysis and bootstrap. The proposed estimation strategy consists of several consecutive steps: first, to reduce a small sample bias resulting from excessive use of instruments I summarize all available information by employing factor analysis and include estimated factors into information set. In the second step I use statistical information criteria to select optimal instruments and eventually I obtain confidence intervals on parameters using bootstrap method. In NKPC context all these methods were used for the first time and can also be used independently. Their combination however provides synergistic effect that helps to improve the properties of estimates and to check the efficiency of given steps. Obtained results suggest that NKPC model can explain Czech inflation dynamics fairly well and provide some support for underlying theory. Among other things the results imply that the policy of disinflation may not be as costly with respect to a loss in aggregate product as earlier versions of Phillips curve would indicate. However, finding a good proxy for real economic activity has proved to be a difficult task. In particular we demonstrated that results are conditional on how the measure is calculated, some measures even showed countercyclical behaviour. This issue -- in the thesis discussed only in passing -- is a subject of future research. In addition to the proposed strategy and provided parameter estimates the thesis brings some partial simulation-based findings. Simulations elaborate on earlier literature on naive bootstrap in GMM context and study performance of bootstrap modifications of unit root and KPSS test.

本研究分別利用傳統 OLS、誤差修正模型以及 Bivariate GARCH 模型研究以摩根台股指數期貨規避台灣股價指數的避險效果，現貨部分除了摩根台股指數現貨之外，亦考慮了台灣加權股價指數，目的在於瞭解摩根指數期貨的避險效果，並提出未來台灣加權股價指數上市後一套研究指數期約避險績效的研究架構。 本研究實證結果發現： (1)將台灣加權股價指數、摩根台股指數現貨以及摩根台股指數期貨的每日收盤價取對數值，並且依照避險期間分為三種情況，利用 ADF(Augmented Dicky and Fuller)進行單根檢定，結果顯示三個時間數列皆非定態(stationary)。 (2)時間數列取一階差分之後，視為指數的報酬率，同樣利用 ADF 進行單根檢定，結果顯示三個時間數列呈現定態(stationary)，亦即時間列服從 I (1)。此時，報酬的迴歸式存在具有實質意義。進行供整合檢定之結果顯示，無論是台灣加權指數與摩根台股指數期貨市場間，或是摩根台股指數之現貨與期貨市場間存在長期穩定之均衡關係。因此欲研究現貨與期貨市場的避險比率，應考慮誤差修正項。 (3)在加權股價指數與摩根指數期貨間避險效果方面： 1.在樣本內實證中，傳統 OLS 除了在避險期間為每日的情況之外，所造成投資組合變異數降低幅度較大，有較好的樣本內避險效果表現。 2.在樣本外實證中，傳統 OLS 無論在何避險期間，所造成投資組合變異數降低幅度較小，其避險效果皆較差。 3.避險誤差均方根比較方面，傳統 OLS 表現較差。 (4)在摩根台股指數現貨與摩根指數期貨間避險效果方面 1.在樣本內實證中，傳統 OLS 在各避險期間，所造成投資組合變異數降低幅度較大，有較好的樣本內避險效果表現。 2.在樣本內實證中，傳統 OLS 無論在何避險期間，其避險效果差皆較差。 3.避險誤差均方根比較方面，同樣以傳統 OLS 表現較差。 / Investors of Taiwan Stock Market have been long lack of hedging tools. SIMEX has provided a new merchant, MSCI Taiwan Index Future on January 9,1997. In addition, Taiwan Futures Exchange is going to run on July, 1998. Though investors are still not familiar with the new derivatives. Futures will be the new markets in Taiwan and it is the right time for us to analyze it. This research use different econometrics methods to check if it is a good hedge tool for the investors. The results are as followed. 1.The time series of MSCI Taiwan Index futures, MSCI Index Spots and Taiwan Weighted Index are not stationary. They are integrated of order 1. 2.There exist cointegrations between MSCI Taiwan Index futures and MSCI Index Spots, in addition to MSCI Taiwan Index futures and Taiwan Weighted Index. 3.OLS Regression, Error Correction Model and Bivariate GARCH Model are applied to find the optimal hedge retio. Among them, the hedge ratios of Bivariate GARCH Model are dynamic while the other two are constant. 4.According to the in-sample hedging effects results, the OLS are outstanding. The low variance of hedging portfolios and the reduction percentage compared to the no-hedged portfolios prove that. 5.Investors may care more about the out-sample results. From the table we know that Error Correction Model and Bivariate GARCH Model perform better than OLS, especially when the time period is longer. 6.When we check the RMSE, we get the same conclusion that OLS is the worst one among the three methods.

中國大陸於1979年開始進行經濟改革，廣開經濟之門，大量吸收外資來活 潑各項經濟建設活動，正逐步邁向計劃商品經濟的新體制。其中，成立中 國鄭州市場的構想，乃至於正式開業，是大陸傳統社會主義的大改變，表 徵以市場機能為中心的資本主義在大陸抬頭，是應計劃經濟體制必需與自 由市場互相協調配合之經改政策的具體結果。中國鄭州商品交易所與上海 金屬交易所、深圳有色金屬交易所並稱為大陸三大期貨市場，占大陸期貨 總交易量的80％，深受舉世所矚目，成功與否，對大陸經改及形成亞太經 濟圈都具有重要意義。通常期貨市場加入純現貨市場經濟體系，對於穩定 價格和經濟發展有其正面貢獻。本文將探討中國大陸現階段如何建立期貨 市場？如何對大陸傳統經濟體制造成影響與挑戰？目前發展到甚麼程度？ 如何善加利用自由經濟體制的市場機能來成功的發展期貨市場？本文欲對 大陸目前尚在初級水準的期貨市場提出意見，甚至期待其能發展成全球性 期貨市場。本文對全中國大陸期貨市場將作一全面性的概觀、對幾個主要 的期貨交易所作一重點式的簡介，然後進入本文重點，亦即對中國鄭州商 品交易所作詳細探討，包括其運作狀態、市場效率性等，以下是本文內容 。時間數列的資產價格大多為具有單根的非穩定性變數的特性已廣被接受 ，非穩性變數使傳統的F-統計量或t-統計量會得出不正確的檢定結果及估 計。本文採用 Engle & Granger(1987)的二階段估計法，首先以 Dickey & Fuller (1981) 的單根檢定 (ADF unit root test) 得出鄭州 交易所及芝加哥交易所的期貨價格為具有單根的時間數列，其次以 Engle & Granger (1987) 的共整合檢定方法，得出對於才自1993年5月28 日成立的中國大陸鄭州商品交易所與自1865年即開始期貨交易的美國芝加 哥期貨交易所 ( CBOT) 同種商品之間，包括小麥、玉米及大豆，不具共 整合關係，推論此二市場目前尚沒有長期穩定均衡關係，亦即此二市場為 區隔性 ( seg- mented) ，而非共整合性 (cointegrated) 。反之，對鄭 州交易所內不同商品的期貨價格作兩兩共整合檢定，呈現相當高的共整合 現象，隱含一種商品的期貨價格可以被另一種商品的期貨價格所預測 (predictability)，違反市場效率性的假說，故本文得出結論：中國大陸 鄭州商品交易所成立至今短短十個月 (截至1994年3月底止之資料)，尚不 具市場效率性。 / It is now widely accepted that financial price series are generally not stationary and consequently, conventional statisti- cal procedures like F-statistic and t-statistic are no longer appropriate for testing market efficiency and estimation. Since nonstationary variables have infinite variance that make the F- test or t-test invalid, the standard hypothesis testing does not apply to time series with unit roots. This article adopts Engle and Granger's (1987) two-stage estimation. Firstly, apply augu- mented Dickey & Fuller unit root test (1981) to the argricultur markets are with unit roots which means both time series variables are nonstationary. Secondly, apply Engle & Granger's (1987) Cointegration Test to test whether the cointegration relationship, including wheat, corn and soybean futures market, between CZCE and CBOT exists or not, the former one is established on May 28th, 1993 in Mainland China and the latter one is established since 1865 in the United States. The result is the wheat, corn and soybean futures prices in these two markets are not cointegrated which implys by now these two markets have no longterm equilibrium relationship, also implys CZCE and CBOT are segmented, not cointegrated. On the contrary, applying Engle & Granger's (1987) Cointegration Tests to test the different argriculture futures market in CZCE, cointegration can not be rejected. That implys one argriculture futures price can be predicted by other argriculture futures price and the market efficiency hypothesis is rejected. Therefore this article has the following conclusion : the empirical results by now presented the rejection of the market efficiency hypothesis for three argriculture products -- wheat, corn, and soybean -- traded on China Zhengzhou Commodities Exchange.

經濟理論明白揭示，在不確定下，金融性資產的選擇不僅要考慮其未來報 酬率的平均值，更需將風險程度納入決策過程中。而最佳風險測度為預測 誤差的變異數(Variance of Forec ast Error)。傳統實証方法均視變異 數為固定常數，實無法掌握變異數具有條件異質性的特點。為了到達此目 的，Engle(1982) 提出向量自迴歸條件異質變異數(ARCH)模型，此模型假 定條件變異數不再是固定常數而是過去干擾項平方的線型函數，為實証方 法上一項偉大的突破。在考慮多個變數的聯立動態體系中，由於跨方程式 間可以互相提供額外的訊息，往往可以增加估計的效率性，直覺上比單變 數的設定更能掌握資料的實際情形。故往後的學者便提出了多元自迴歸條 件異質變異數(Multivariate ARCH) 模型，此一模型亦有其缺點存在，因 其待估計參數過多，形成自由度嚴重減少，將導致估計值缺乏效率性。所 以如何利用可獲得的有限資料對模型進行更有效率的估計方式，此為研究 Multivaria te ARCH的重要課題。本文將對Multivariate ARCH做一系列 的介紹，並利用VAR 的貝氏方法對參數進行估計。而多元因素AR CH模型 也是探討的重點。