This dissertation examines the causal relationship between inward foreign direct investment (FDI) and economic growth (GDP) in SADC countries. The study investigates, within a panel data context, whether causation is short-term, long-term or both; and explores whether the causal relationship between the two variables differs according to income level. The study covered a panel of 15 SADC countries over the period 1980-2012. In order to assess whether the causal relationship between FDI inflows and economic growth is dependent on the level of income, the study divided the SADC countries into two groups, namely, the low-income and the middleincome countries. The study used the recently developed panel data analysis methods to examine this causal relationship. It adopted a three stage approach, which consists of panel unit root, panel cointegration and Granger causality to examine the dynamic causal relationship between the two variables. Panel unit root results show that both variables in the two SADC country groups were integrated of order one. Panel cointegration tests showed that the variables for low-income country group were not cointegrated, while the variables for the middle-income countries were cointegrated. Since the low-income country group panels were not cointegrated, Grangercausality tests were conducted within a VAR framework, while causality tests for the middleincome country group were conducted within an ECM framework. Panel Granger causality results for the low-income countries showed no evidence of causality in either direction. However, for the middle-income countries’ panel, there was evidence of a unidirectional causal flow from GDP to FDI in both the long- and short- run. The study concludes that the FDI-led growth hypothesis does not apply to SADC countries. The results imply that the recent high economic growth rates recorded in the SADC region, especially middle-income countries, have been attracting FDI. In other words, it is economic growth that drives FDI inflows into the SADC region, and not vice versa. These findings have profound policy implications for the SADC region at large and individual countries. / Economics / M. Com. (Economics)

自Nelson和Plosser (1982)後，研究經濟資料是否具有單位根現象，已成為近二十年來熱門且重要的課題。因 為資料性質的不同(恆定或非恆定)，對實證計量模型的設定、統計推論以及原理論的發展有深遠的影響。與傳 統探討單一時間數列之單位根的論文不同的是，本篇論文將橫斷面的資料擴大，探討混合型資料的單位根現象 ( Panel Unit Root )。就此課題，文獻上已有兩個不同的檢定方法: Levin、Lin和Chu (1997)的LLC檢定法以及Im、 Pesaran和Shin (1995)的IPS檢定法。 我們的研究，有別於以上兩者，是從「概似比」的角度(likelihood ratio) 和應用檢定共積關係的Johansen (1988)「Trace檢定」，建構新的單位根檢定統計量。首先於文中推導出，「Trace檢定」可用於檢測單一時間數 列的單位根現象。進而，再將橫斷面資料擴大，採用mean group方法，加總平均每個橫斷面時間數列的「Trace 檢定」統計量，形成混合型資料之單位根檢定統計量 。根據中央極限定理，標準化後的 檢定統計量，極限上 收斂至標準常態分配。此外，我們也推導得出 檢定統計量與傳統ADF、LLC以及IPS檢定統計量極限上的關係。 最後，我們以「蒙地卡羅」模擬方法，分析小樣本下「型一誤差」與「檢定力」的表現。發現新的混合型資 料之單位根檢定統計量表現優良，近似於標準常態分配。故在做混合型資料的單位根分析時，採用 檢定統計 量，可得到較精確的推論。

This study tests for the market efficiency of the Nairobi Securities Exchange (NSE) after the year 2000 to determine the effect of technological advancements on market efficiency. Data that is used is the NSE 20 share index over the period 2001 to 2015; and the NSE All Share Index (NSE ASI) from its initiation during 2008 to 2015. We cannot accept the Efficient Market Hypothesis (EMH) for the NSE using the serial correlation test, the unit root tests and the runs test. However, we can accept the EMH for the more robust variance ratio test. Overall, the results of the market efficiency are mixed. The most significant finding is that the efficiency of the NSE has increased since the year 2000 which suggests that advancements in technology have contributed to the increase in the market efficiency of the NSE. / Business Management / M. Com. (Business Management)

This thesis considers new methods that exploit recent developments in computer technology to address three extant problems in the area of Finance and Econometrics. The problem of Asian option pricing has endured for the last two decades in spite of many attempts to find a robust solution across all parameter values. All recently proposed methods are shown to fail when computations are conducted using standard machine precision because as more and more accuracy is forced upon the problem, round-off error begins to propagate. Using recent methods from numerical analysis based on multi-precision arithmetic, we show using the Mathematica platform that all extant methods have efficacy when computations use sufficient arithmetic precision. This creates the proper framework to compare and contrast the methods based on criteria such as computational speed for a given accuracy. Numerical methods based on a deformation of the Bromwich contour in the Geman-Yor Laplace transform are found to perform best provided the normalized strike price is above a given threshold; otherwise methods based on Euler approximation are preferred. The same methods are applied in two other contexts: the simulation of stable distributions and the computation of unit root densities in Econometrics. The stable densities are all nested in a general function called a Fox H function. The same computational difficulties as above apply when using only double-precision arithmetic but are again solved using higher arithmetic precision. We also consider simulating the densities of infinitely divisible distributions associated with hyperbolic functions. Finally, our methods are applied to unit root densities. Focusing on the two fundamental densities, we show our methods perform favorably against the extant methods of Monte Carlo simulation, the Imhof algorithm and some analytical expressions derived principally by Abadir. Using Mathematica, the main two-dimensional Laplace transform in this context is reduced to a one-dimensional problem.

本研究目的在於探討投資等級債券信用價差是否存在外溢效果。信用價差是建構各種信用衍生性金融商品的基礎，惟目前學術界及業界都著眼在信用價差的拆解。信用價差可拆解成預期違約損失、稅的溢酬及信用風險溢酬。投資等級債券的信用價差來自於預期違約損失、稅的溢酬的部分較少，絕大多數來自於信用風險溢酬。信用風險溢酬係系統性影響信用價差的因素，此因素造成不同投資等級債券的信用價差間具有共整合的現象，進而引發外溢效果。然而並無人對於信用價差外溢效果作一深入探討。本研究利用目前學術界盛行的Panel模型的研究方法，對各種投資等級的債券的信用價差進行Panel Unit Root Tests、Panel Cointegration Tests及Panel Spillover Effect Tests，以求發現債券信用價差外溢效果存在與否的證據。 本文以iBoxx Index成份債券作為研究標的，利用Panel研究方法得到以下結論: 1.根據研究結果顯示，各種信評等級的債券的信用價差存在單根問題。 2.不同投資等級信評債券的信用價差擁有共整合關係。 3.不同投資等級信用評等的債券間信用價差外溢效果存在。且愈是相 鄰信評等級債券的外溢效果愈為顯著，例如BBB等級信用價差發生變動引發信評AAA等級信用價差變動的幅度便沒有AA等級信用價差變動引發AAA等級信用價差變動來得強烈。外溢效果係不對稱，當最高投資等級信評發生變動時，最低投資等級債券變動最為激烈;而最低投資等級信評發生波動時，最高投資等級債券發生變動的幅度就較小。 4.本研究支持不同債信評等的債券存在同向的外溢效果。 / This paper investigates the spillover effect in the investment grade bonds using the recently developed Panel Unit Root Tests, Panel Cointegrations Tests, Panel FMOLS and Panel DOLS techniques. Investment grade bonds’ credit spreads are found to be nonstationary and to be cointegrated in panels. This paper finds evidence of spillover effects.

Cette thèse est dévolue à l'étude de certaines propriétés asymptotiques du processus autorégressif d'ordre p. Ce dernier qualifie communément une suite aléatoire $(Y_{n})$ définie sur $\dN$ ou $\dZ$ et entièrement décrite par une combinaison linéaire de ses $p$ valeurs passées, perturbée par un bruit blanc $(\veps_{n})$. Tout au long de ce mémoire, nous traitons deux problématiques majeures de l'étude de tels processus : l'\textit{autocorrélation résiduelle} et la \textit{stationnarité}. Nous proposons en guise d'introduction un survol nécessaire des propriétés usuelles du processus autorégressif. Les deux chapitres suivants sont consacrés aux conséquences inférentielles induites par la présence d'une autorégression significative dans la perturbation $(\veps_{n})$ pour $p=1$ tout d'abord, puis pour une valeur quelconque de $p$, dans un cadre de stabilité. Ces résultats nous permettent d'apposer un regard nouveau et plus rigoureux sur certaines procédures statistiques bien connues sous la dénomination de \textit{test de Durbin-Watson} et de \textit{H-test}. Dans ce contexte de bruit autocorrélé, nous complétons cette étude par un ensemble de principes de déviations modérées liées à nos estimateurs. Nous abordons ensuite un équivalent en temps continu du processus autorégressif. Ce dernier est décrit par une équation différentielle stochastique et sa solution est plus connue sous le nom de \textit{processus d'Ornstein-Uhlenbeck}. Lorsque le processus d'Ornstein-Uhlenbeck est lui-même engendré par une diffusion similaire, cela nous permet de traiter la problématique de l'autocorrélation résiduelle dans le processus à temps continu. Nous inférons dès lors quelques propriétés statistiques de tels modèles, gardant pour objectif le parallèle avec le cas discret étudié dans les chapitres précédents. Enfin, le dernier chapitre est entièrement dévolu à la problématique de la stationnarité. Nous nous plaçons dans le cadre très général où le processus autorégressif possède une tendance polynomiale d'ordre $r$ tout en étant engendré par une marche aléatoire intégrée d'ordre $d$. Les résultats de convergence que nous obtenons dans un contexte d'instabilité généralisent le \textit{test de Leybourne et McCabe} et certains aspects du \textit{test KPSS}. De nombreux graphes obtenus en simulations viennent conforter les résultats que nous établissons tout au long de notre étude. / This thesis is devoted to the study of some asymptotic properties of the $p-$th order \textit{autoregressive process}. The latter usually designates a random sequence $(Y_{n})$ defined on $\dN$ or $\dZ$ and completely described by a linear combination of its $p$ last values and a white noise $(\veps_{n})$. All through this manuscript, one is concerned with two main issues related to the study of such processes: \textit{serial correlation} and \textit{stationarity}. We intend, by way of introduction, to give a necessary overview of the usual properties of the autoregressive process. The two following chapters are dedicated to inferential consequences coming from the presence of a significative autoregression in the disturbance $(\veps_{n})$ for $p=1$ on the one hand, and then for any $p$, in the stable framework. These results enable us to give a new light on some statistical procedures such as the \textit{Durbin-Watson test} and the \textit{H-test}. In this autocorrelated noise framework, we complete the study by a set of moderate deviation principles on our estimates. Then, we tackle a continuous-time equivalent of the autoregressive process. The latter is described by a stochastic differential equation and its solution is the well-known \textit{Ornstein-Uhlenbeck process}. In the case where the Ornstein-Uhlenbeck process is itself driven by an Ornstein-Uhlenbeck process, one deals with the serial correlation issue for the continuous-time process. Hence, we infer some statistical properties of such models, keeping the parallel with the discrete-time framework studied in the previous chapters as an objective. Finally, the last chapter is entirely devoted to the stationarity issue. We consider the general autoregressive process with a polynomial trend of order $r$ driven by a random walk of order $d$. The convergence results in the unstable framework generalize the \textit{Leybourne and McCabe test} and some angles of the \textit{KPSS test}. Many graphs obtained by simulations come to strengthen the results established all along the study.