Das Kausalitaetskonzept von Granger und die Impuls-Antwort-Analyse sind zwei Konzepte, die haeufig verwendet werden, um kausale Beziehungen zwischen zwei Variablen in vektorautoregressiven (VAR) Modellen zu untersuchen. Wenn das VAR Modell mehr als zwei Variablen umfasst, besteht eine Erweiterung des Standard Granger Kausalitaetskonzepts darin, Kausalitaet an hoeheren Prognosehorizonten zu messen. Die Kausalitaetsbeziehungen unter diesem erweiterten Granger Kausalitaetskonzept werden mit denen bei Standard Granger Kausalitaet (Ein-Schritt-Prognose) und mit Kausalitaet im Sinne der Impuls-Antwort-Analyse verglichen. Es wird insbesondere dargestellt, inwiefern das erweiterte Granger Kausalitaetskonzept als Verallgemeinerung der letztgenannten Konzepte aufgefasst werden kann. Wenn Kausalitaet an Prognosehorizonten groesser als eins gemessen wird und das VAR Modell mehr als zwei Variablen umfasst, impliziert die Nullhypothese, dass eine Variable nicht kausal fuer eine andere Variable sei, nichtlineare Restriktionen auf die VAR Koeffizienten. (In nichtstationaeren VAR Modellen treten nichtlineare Restriktionen sogar schon unter dem Standard Granger Kausalitaetskonzept auf.) Aufgrund der speziellen Form der Restriktionen kann es vorkommen, dass die Standard Wald Statistik nicht mehr die uebliche, asymptotische Chiquadrat-Verteilung hat. Dieses Problem wird im allgemeinen in der Praxis ignoriert. Beispiel 4.1, Proposition 4.1 und Korollar 4.1 zeigen jedoch, dass dieses Problem nicht irrelevant ist. Zwei Loesungen werden in Proposition 5.1 und Proposition 5.2 in Form eines randomisierten Wald Tests sowie eines Wald Tests mit verallgemeinerter Inverse angeboten. In einer anschliessenden kleinen Simulationsstudie werden Groesse und Macht dieser modifizierten Wald Tests relativ zu der des Standard Wald Tests untersucht fuer verschiedene stationaere trivariate VAR(1)-Modelle. In einem kurzen Ueberblick werden zudem Vor- und Nachteile alternativer Testverfahren (Bootstrap, sequentielle Tests) zusammengefasst. / The concepts of standard Granger causality and impulse response analysis are often used to investigate causal relationships between variables in vector autoregressive (VAR) models. In VAR models with more than two variables, the concept of standard Granger causality can be extended by studying prediction improvement at forecast horizons greater than one. The causal relationships which arise under this extended Granger causality concept are compared to those arising under the standard Granger causality concept (one-step forecasts) and those arising with impulse-response-analysis. In particular, it is illustrated inhowfar the extended Granger causality concept can be understood as a generalization of the standard Granger causality concept and even of impulse-response-analysis. If causality is measured at forecast horizons greater than one, and if there are more than two variables in the VAR system, the null hypothesis that one variable is not causal for another variable implies restrictions which are a nonlinear function of the VAR coefficients. (In nonstationary VAR models, nonlinear restrictions already arise under the standard Granger causality concept.) Due to the special form of the restrictions, the standard Wald test may no longer have the usual asymptotic chisquare-distribution under the null hypothesis. This problem is commonly neglected in practice. However, Example 4.1, Corollary 4.1 and Proposition 4.1 of this thesis illustrate that this problem is not irrelevant. Furthermore, Propositions 5.1 and 5.2 show that this problem may be overcome, at least in stationary VAR models, by using either a randomized Wald test or a Wald test with generalized inverse. Size and Power of these modified Wald tests relative to the standard Wald test are investigated in a small simulation study for different stationary, trivariate VAR(1) models. Moreover, the pros and cons of alternative testing strategies (bootstrap, sequential tests) are summarized in a brief overview.

This thesis explores the price determinants of Bitcoin using a macroeconomic model based on the economic equation of exchange presented by Joseph Wang (2014). The thesis provides a concise and structured introduction to Bitcoin and a comprehensive literature review on Bitcoin. The analysis begins with the application of the functions of money to Bitcoin, arguing that while Bitcoin does fulfill the three classical functions of money to a certain extent, its use remains mainly as a speculative instrument. Wang's model is criticized and amended to reflect the realities of empirically analyzing the Bitcoin market. Using the daily number of transactions and Bitcoin days destroyed as proxies for economic activity and inactivity - to measure Bitcoin's velocity on the block chain - vector autoregression modelling is used to determine if there is Granger causality between the price of bitcoin and the two proxies. The results demonstrate that there is a bidirectional Granger-causal relationship between Bitcoin days destroyed and the price of bitcoin and that there is none between the daily number of transactions and the price of bitcoin; proving Wang's two main assumptions. Impulse- response functions are provided to illustrate and discuss this bidirectional relationship. The results are in line with the...

This study examined the effects of government expenditure on different components of economic growth in South Africa using quarterly data from the period 1970Q1 to 2016Q4. The six key policy variables employed in the analysis were derived from the Ram (1986) production model and the New Growth Path (NGP), a macroeconomic framework designed to address the main challenges (unemployment, poverty and inequality) facing the economy as a result of its political past. The analysis of the relationship was carried out using the VECM while the findings from the analysis revealed that though there exists a long-run equilibrium relationship among the variables. The long-run estimates showed that aggregate private consumption expenditure and employment-to-population ratio are significant but negatively, related to economic growth. However, the net inflows of foreign direct investment and gross fixed capital formation are negatively related to gross government expenditure. This implies that excessive public capital expenditure might reduce the positive impact of the two variables on economic growth. The study therefore suggests that government should consider increasing its expenditure on the significant variables that support labour and capital development, in order to enhance economic growth in South Africa. / Economics

Thesis (M.Com (Economics)) -- University of Limpopo, 2018 / This study investigates the impact of capital flight and investment on economic growth in South Africa using time series data from 1986 to 2016. It employs the Auto Regressive Distributed Lag (ARDL) bounds testing procedure and the Granger causality test as a method of analysis. The empirical findings reveal that the variables are cointegrated which is an indication of the existence of a long run relationship among them. It was further discovered that capital flight had a negative long run relationship with economic growth while investment showed a positive long run relationship with economic growth. The terms of trade and inflation which were added to the model as control variable were also found to have a significantly positive influence on economic growth. The Granger causality indicated a bidirectional relationship between inflation and economic growth, while the terms of trade is found to have a unidirectional relationship with economic growth and capital investment respectively. The results are in line with the neo-classical growth model and the accelerator theory of investment.

Seminal papers of Solow (1957) and Swan (1956) stimulated debate among economists on the role of technical change in productivity improvements and for that matter economic growth. The consensus is that technological change accounts for a significant proportion of gross national product (GNP) growth in industrialised economies. In the case of Australia, the aggregate productivity performance was poor in the 1970s and 1980s, but picked up very strongly by the 1990s, and was above the OECD average growth level for the first time in its productivity growth history. However, this high productivity growth rate could not be sustained and Australia started to experience a slowdown in productivity growth since 2000. This study empirically measures the performance of productivity in Australia’s economy for the period 1950-2005, using an econometric approach. Time-series data are used to develop econometric models that capture the dynamic interactions between GDP, fixed capital, labour units, human capital, foreign direct investment (FDI) and information and communication technology (ICT). The Johansen (1988) cointegration techniques are used to establish a long-run steady-state relation between or among economic time series. The econometric analysis pays careful attention to the time-series properties of the data by conducting unit root and conintegration tests for the variables in the system. / This study finds that Australia experienced productivity growth in the 1950s, a slow down in the mid 1960s, a very strong productivity growth in the mid 1990s and another slowdown from 2000 onwards. The study finds evidence that human capital, FDI and ICT are very strong determinants of long-run GDP and productivity growth in Australia. The study finds that the three, four and the five factor models are likely to give better measures of productivity performance in Australia as these models recognise human capital, FDI and ICT and include them as separate factors in the production function, This study finds evidence that the previous studies on the Australia’s productivity puzzle have made a very significant omission by not considering human capital, FDI and ICT as additional exogenous variables and by excluding them from the production function for productivity analysis.

價量關係研究於金融市場甚豐，然於台灣之住宅新推個案市場則相當匱乏，因此本研究關注台灣住宅新推個案市場之價量關係，考量住宅空間次市場差異，區分為內部關係─價量關係，以及外部關係─價／量波及效果。研究以全國及五大都會區為（台北市、台北縣、桃竹地區、台中都會區及南高都會區）為空間範圍；1996年第1季至2009第4季之可能成交價、成交量資料，運用時間序列分析方法，釐清住宅空間次市場內部之價量關係是否存在差異，以及次市場間成交價／量是否存在相互影響的效果，以提供預測市場價量趨勢之參考。 研究結果顯示台北市之成交量領先成交價3期，價量交互影響程度較其他地區大，可知台北市住宅市場之成交量變動在住宅市場趨勢預測中更為關鍵；南高都會區之價量存在共整合關係，表示價量調整具長期均衡，背離程度有限；台北縣、桃竹地區及台中都會之價量則無明顯領先落後關係，價量關係相對薄弱。波及效果之研究結果顯示成交價之波及效果主要由台北都會區擴散至其他都會區，影響方向為單向且範圍較大；成交量則以相對鄰近之都會區為影響範圍，影響主要為雙向，但範圍較小。本研究認為台灣住宅市場過度關注價格訊息，然而更應重視成交量變化的掌握，並關注住宅空間次市場基本結構之差異，避免使消息面造成的過度預期成為主導市場的力量。 / There are numerous researches in stock markets and finance, but few in Taiwan newly construction and pre-sale housing markets. Using the Cathay Real Estate Index Quarterly Reports for the period 1996-2009 and applying Granger causality test, the thesis examines price and volume relationship in five metropolises (Taipei City, Taipei County, Taoyuan-Hsinchu, Taichung Metropolis and Tainan-Kaohsiung) in Taiwan. And with the concern of the differences of housing submarkets, the price and volume relationship is classified as intra-relationship and inter-relationship. The former is price and volume relationship in a certain metropolis, the later is the ripple effects of housing price or trading volume between metropolises. The result of intra-relationship shows that housing price Granger-cause the trading volume in Taipei city. That is, volume provides useful information to predict future price. And there is a long-run relationship in Tainan-Kaohsiung metropolis. From the aspect of inter-relationship, housing price changes first in Taipei City and Taipei County; trading volumes have mutual ripple effect between two neighboring metropolises. The results of the research are useful for housing market participants: We should keep an eye on the changes of trading volume. Also the structure of the submarket is fundamental to form the investment strategies.

Bakgrund och Problem: Aktiemarknaden påverkas både av inhemska och utländska faktorer. Därför är det av intresse att se vilka makroekonomiska variabler som påverkar den svenska aktiemarknaden. Anledningen till att Sverige har valts som den geografiska punkten är att det är av intresse att se hur ett litet land som Sverige, som har en öppen ekonomi påverkas av de utvalda makroekonomiska variablerna. Syfte: Syftet med uppsatsen är att med hjälp av information samt analys, studera hur de olika makroekonomiska variablerna påverkar den inhemska aktiemarknaden. Olika faktorer som påverkar aktiemarknaden kommer att lyftas fram för att i sin tur även se till de olika branscherna. Metod: Då data enbart består av hämtning av tidigare information fokuseras det enbart på sekundärdata i form av historiska siffror samt historiska undersökningar. De statistiska tester som tillämpas är Granger Causality test, Johansens Cointegration test, Impulse Response Function test, ADF test, KPSS test, Mulitpel regression. Slutsats: Med de resultat som presenterades i denna studie, skulle vi nog inte kunna säga att vi har ett svar över vilka aktier en investerare ska införskaffa. Dock skulle vi kunna poängtera att den potentiella investeraren bör ha dessa variabler i beaktning vid beslut. Genom att studera dessa variabler kan man få en känsla om vilket håll variablerna kommer att röra sig och på så sätt säga att de kan påverka aktieindexen. Att bara kolla på de makroekonomiska variabler som denna studie belyser räcker inte för att förstå hur aktieindex kommer att se ut i framtiden, men det är en bit på vägen till att förstå aktiemarknadens rörelse.

Functional Magnetic Resonance Imaging (fMRI) is one of the best techniques for neuroimaging and has revolutionized the way to understand the brain functions. It measures the changes in the blood oxygen level-dependent (BOLD) signal which is related to the neuronal activity. Complexity of the data, presence of different types of noises and the massive amount of data makes the fMRI data analysis a challenging one. It demands efficient signal processing and statistical analysis methods.  The inference of the analysis is used by the physicians, neurologists and researchers for better understanding of the brain functions.      The purpose of this study is to design a toolbox for fMRI data analysis. It includes methods to detect the brain activity maps, estimation of the hemodynamic response (HDR) and the connectivity of the brain structures. This toolbox provides methods for detection of activated brain regions measured with Bayesian estimator. Results are compared with the conventional methods such as t-test, ordinary least squares (OLS) and weighted least squares (WLS). Brain activation and HDR are estimated with linear adaptive model and nonlinear method based on radial basis function (RBF) neural network. Nonlinear autoregressive with exogenous inputs (NARX) neural network is developed to model the dynamics of the fMRI data.  This toolbox also provides methods to brain connectivity such as functional connectivity and effective connectivity.  These methods are examined on simulated and real fMRI datasets.

自從2005年7月21日中國人民銀行宣布大幅改革人民幣匯率形成機制後，中國境內人民幣即期匯率便開始大幅升值。為穩定其在改革起步階段的人民幣即期與遠期市場，國家外匯管理局遂在2006年10月20日發布通知，禁止境內機構參與海外人民幣NDF業務。另外，早在2005年人民幣匯率改革之前，中國人民銀行在2003年11月就已經在香港提供人民幣清算業務，逐漸形成「香港離岸人民幣即期匯率」(CNH)。因此本篇論文旨在探討境內外人民幣的互動關係，藉由不同政策發佈時點前後的比較，歸納出境內外人民幣即期與遠期匯率之間的相互影響關係與影響程度。 本篇論文選取時間分別為2006年6月7日至2007年3月20日及2009年3月2日至2013年3月29日兩段期間之境內外人民幣每日收盤匯率，研究方法以向量自我迴歸為主，搭配ADF單根檢定、Johansen共整合檢定、Granger因果關係檢定及衝擊反應分析等進行人民幣NDF和即期匯率互動關係的探討。 實證結果顯示：(一) NDF監管政策並沒有完全阻隔境內外之連結，反而在境外投資人對沖人民幣風險的超額需求下使一月期人民幣NDF與境內人民幣即期匯率(CNY)之關係更緊密。(二) 離岸人民幣即期匯率(CNH)逐漸接軌境內人民幣即期匯率(CNY)，且境內信息優勢仍然明顯。(三) CNH仍無法完全取代NDF的地位。 隨著人民幣國際化腳步不斷加速，未來可預期人民幣將成為亞太地區的主要領導貨幣，因而了解境內外人民幣的互動與中國官方的匯率政策之間的關係變顯得十分重要，希望藉由本篇論文的撰寫對後續的研究能有所幫助。

Communicating bits over a network is expensive. Therefore, cryptosystems that transmit as little data as possible are valuable. This thesis studies several cryptosystems that require significantly less bandwidth than conventional analogues. The systems we study, called torus-based cryptosystems, were analyzed by Karl Rubin and Alice Silverberg in 2003 [RS03]. They interpreted the XTR [LV00] and LUC [SL93] cryptosystems in terms of quotients of algebraic tori and birational parameterizations, and they also presented CEILIDH, a new torus-based cryptosystem. This thesis introduces the geometry of algebraic tori, uses it to explain the XTR, LUC, and CEILIDH cryptosystems, and presents torus-based extensions of van Dijk, Woodruff, et al. [vDW04, vDGP⁺05] that require even less bandwidth. In addition, a new algorithm of Granger and Vercauteren [GV05] that attacks the security of torus-based cryptosystems is presented. Finally, we list some open research problems.