A number of developing countries have been on a quest to attract foreign direct investment (FDI) with the intention of increasing capital inflow through technological spillovers and transfer of managerial skills. FDI can increase economic growth and development of a country by creating employment, and by doing so, increasing economic activity that will lead to economic growth. South Africa is one of the economies that strive to attract more FDI inflows into the country to be able to improve its economy, and the country has adopted policies that drive the motive to attract FDI inflows. This study investigated the effect of FDI on sectoral growth over the period 1970–2014. The purpose was to find out where in the three key sectors of South Africa FDI is more significant. The review of theoretical and empirical literature on FDI revealed that FDI has a diverse effect on economic growth, both in developed and developing countries. Theoretical literature analysed the behaviour of multinational firms and the motive behind multinationals investing in foreign countries. According to Dunning (1993), firms have four motives to decide to produce abroad, namely natural resource-seeking, market-seeking, efficiency-seeking and strategic asset-seeking. Empirical studies on sectors show that FDI inflows affect different sectors in different ways, and that the agricultural sector does not usually gain from FDI inflows, whereas subsectors in the industry and services sector grow from receiving FDI inflows. Sectoral analysis revealed that the services sector receives more FDI inflows, when compared to the agriculture and industry sector. The study followed an econometric analysis technique to test the effect of FDI inflows on the agriculture, industry and services sectors. The augmented Dickey–Fuller and Phillips–Perron tests were used to test for unit root. Both tests revealed that variables were not stationary at level, but that they become stationary at first difference. Vector autoregressive (VAR) models were estimated, and four types of diagnostic tests were performed on them to check the fitness of the models. The tests showed that residuals of the estimated VARs were robust and well behaved. The Johansen cointegration test suggested there is cointegration and that there is a long-run relationship between variables. Following the existence of cointegration, the estimated Vector error correction model (VECM) results showed that FDI has a significant effect on the services and industry sector, but has a negative effect on the agricultural sector. Impulse response analysis results revealed the correct signs, and confirmed the VECM results. FDI inflows explain a small percentage of growth in agriculture and industry, but a sizable and significant percentage in the services sector. / Economics / M. Com. (Economics)

This dissertation can be broadly divided into two independent parts. The first three chapters analyse issues related to temporal and contemporaneous aggregation of econometric models. The fourth chapter contains an application of Bayesian techniques to investigate whether the post transition fiscal policy of Poland is sustainable in the long run and consistent with an intertemporal budget constraint.<p><p><p>Chapter 1 surveys the econometric methodology of temporal aggregation for a wide range of univariate and multivariate time series models. <p><p><p>A unified overview of temporal aggregation techniques for this broad class of processes is presented in the first part of the chapter and the main results are summarized. In each case, assuming to know the underlying process at the disaggregate frequency, the aim is to find the appropriate model for the aggregated data. Additional topics concerning temporal aggregation of ARIMA-GARCH models (see Drost and Nijman, 1993) are discussed and several examples presented. Systematic sampling schemes are also reviewed.<p><p><p>Multivariate models, which show interesting features under temporal aggregation (Breitung and Swanson, 2002, Marcellino, 1999, Hafner, 2008), are examined in the second part of the chapter. In particular, the focus is on temporal aggregation of VARMA models and on the related concept of spurious instantaneous causality, which is not a time series property invariant to temporal aggregation. On the other hand, as pointed out by Marcellino (1999), other important time series features as cointegration and presence of unit roots are invariant to temporal aggregation and are not induced by it.<p><p><p>Some empirical applications based on macroeconomic and financial data illustrate all the techniques surveyed and the main results.<p><p>Chapter 2 is an attempt to monitor fiscal variables in the Euro area, building an early warning signal indicator for assessing the development of public finances in the short-run and exploiting the existence of monthly budgetary statistics from France, taken as "example country". <p><p><p>The application is conducted focusing on the cash State deficit, looking at components from the revenue and expenditure sides. For each component, monthly ARIMA models are estimated and then temporally aggregated to the annual frequency, as the policy makers are interested in yearly predictions. <p><p><p>The short-run forecasting exercises carried out for years 2002, 2003 and 2004 highlight the fact that the one-step-ahead predictions based on the temporally aggregated models generally outperform those delivered by standard monthly ARIMA modeling, as well as the official forecasts made available by the French government, for each of the eleven components and thus for the whole State deficit. More importantly, by the middle of the year, very accurate predictions for the current year are made available. <p><p>The proposed method could be extremely useful, providing policy makers with a valuable indicator when assessing the development of public finances in the short-run (one year horizon or even less). <p><p><p>Chapter 3 deals with the issue of forecasting contemporaneous time series aggregates. The performance of "aggregate" and "disaggregate" predictors in forecasting contemporaneously aggregated vector ARMA (VARMA) processes is compared. An aggregate predictor is built by forecasting directly the aggregate process, as it results from contemporaneous aggregation of the data generating vector process. A disaggregate predictor is a predictor obtained from aggregation of univariate forecasts for the individual components of the data generating vector process. <p><p>The econometric framework is broadly based on Lütkepohl (1987). The necessary and sufficient condition for the equality of mean squared errors associated with the two competing methods in the bivariate VMA(1) case is provided. It is argued that the condition of equality of predictors as stated in Lütkepohl (1987), although necessary and sufficient for the equality of the predictors, is sufficient (but not necessary) for the equality of mean squared errors. <p><p><p>Furthermore, it is shown that the same forecasting accuracy for the two predictors can be achieved using specific assumptions on the parameters of the VMA(1) structure. <p><p><p>Finally, an empirical application that involves the problem of forecasting the Italian monetary aggregate M1 on the basis of annual time series ranging from 1948 until 1998, prior to the creation of the European Economic and Monetary Union (EMU), is presented to show the relevance of the topic. In the empirical application, the framework is further generalized to deal with heteroskedastic and cross-correlated innovations. <p><p><p>Chapter 4 deals with a cointegration analysis applied to the empirical investigation of fiscal sustainability. The focus is on a particular country: Poland. The choice of Poland is not random. First, the motivation stems from the fact that fiscal sustainability is a central topic for most of the economies of Eastern Europe. Second, this is one of the first countries to start the transition process to a market economy (since 1989), providing a relatively favorable institutional setting within which to study fiscal sustainability (see Green, Holmes and Kowalski, 2001). The emphasis is on the feasibility of a permanent deficit in the long-run, meaning whether a government can continue to operate under its current fiscal policy indefinitely.<p><p>The empirical analysis to examine debt stabilization is made up by two steps. <p><p>First, a Bayesian methodology is applied to conduct inference about the cointegrating relationship between budget revenues and (inclusive of interest) expenditures and to select the cointegrating rank. This task is complicated by the conceptual difficulty linked to the choice of the prior distributions for the parameters relevant to the economic problem under study (Villani, 2005).<p><p>Second, Bayesian inference is applied to the estimation of the normalized cointegrating vector between budget revenues and expenditures. With a single cointegrating equation, some known results concerning the posterior density of the cointegrating vector may be used (see Bauwens, Lubrano and Richard, 1999). <p><p>The priors used in the paper leads to straightforward posterior calculations which can be easily performed.<p>Moreover, the posterior analysis leads to a careful assessment of the magnitude of the cointegrating vector. Finally, it is shown to what extent the likelihood of the data is important in revising the available prior information, relying on numerical integration techniques based on deterministic methods.<p> / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Une crise financière et économique sans précèdent est apparue aux Etats-Unis en 2007, a progressé rapidement et s’est propagée à de nombreux pays dans le monde. L’instrument budgétaire a été largement utilisé : dans un contexte de contagion financière, les gouvernements ont dû réagir en adoptant dans un premier temps des mesures visant à relancer l'économie, puis, dans un deuxième temps, face à l’endettement croissant, des mesures de stabilisation économique. L'objectif de cette thèse est de mettre en évidence l'importance des caractéristiques spécifiques à la fois régionales et nationales dans la prise de décision publique visant à stimuler la croissance économique. La thèse analyse la relation entre le PIB et le chômage, ainsi que les effets des programmes de relance budgétaire. Dans la première partie, la loi d'Okun est examinée, au niveau régional, dans trois pays émergents d’Europe Centrale et de l’Est. Dans la deuxième partie, un éclairage particulier est porté sur le concept de multiplicateur budgétaire et ses implications de politique économique. Dans la troisième partie, les multiplicateurs budgétaires sont calculés dans des pays émergents, en particulier ceux des régions méditerranéennes et d’Europe Centrale et de l’Est. La thèse mobilise les outils de l’économétrie sur séries temporelles et sur panels de longue durée. / An unprecedented financial and economic crisis irrupted in the US in 2007, and has rapidly grown and spread to many countries around the world. The financial instrument has been widely used: in a context of financial contagion, governments have initially reacted by adopting measures to revive the economy, and then, secondly, facing mounting debt, implemented economic stabilization policies. The goal of this thesis is to highlight the importance of specific features both at regional and national level in the public decision making to stimulate economic growth. The thesis analyses the relationship between GDP and unemployment, as well as the effects of fiscal stimuli. In the first part, Okun’s law is examined at regional level in three emerging Central and Eastern European countries. In the second part, the emphasis is given to the concept of fiscal multiplier and its policy implications. In the third part, fiscal multipliers are assessed in emerging countries, particularly those of the Mediterranean and the Central and Eastern Europe regions. The thesis makes use of time series and panel econometrics methods.

Doctor of Philosophy / Department of Economics / Lance J. Bachmeier / This dissertation investigates the long run and short run relationships between Saudi stock market returns and eight macroeconomic variables. We investigate the ability of these variables to predict the level and volatility of Saudi stock market returns. A wide range of Vector autoregression (VAR) and generalized autoregressive conditional heteroskedasticity (GARCH) models estimated and interpreted. A Johansen-Juselius cointegration test indicates a positive long run relationship between the Saudi stock price index and the M2 money supply, bank credit, and the price of oil, and a negative long run relationship with the M1 money supply, the short term interest rate, inflation, and the U.S. stock market. An estimated vector error correction model (VECM) suggests significant unidirectional short run causal relationships between Saudi stock market returns and the money supply and inflation. The VECM also finds a significant long run causal relationship among the macroeconomic variables in the system. The estimated speed of adjustment indicates that the Saudi stock market converges to the equilibrium within half a year. Granger causality tests show no causal relationship between Saudi stock market returns and the exchange rate. Impulse response function analysis shows no significant relationship between Saudi stock market returns and the macroeconomic variables. Forecast error variance decompositions suggest that 89% of the variation in Saudi stock market returns is attributable to its own shock, which implies that Saudi stock market returns are largely independent of the macroeconomic variables in the system. Finally, a GARCH-X model indicates a significant relationship between volatility of Saudi stock returns and short run movements of macroeconomic variables. Implications of this study include the following. (i) Prediction of stock market returns becomes more difficult as the volatility of the macroeconomic variables increases in the short run. (ii) Investors should look at the systematic risks revealed by these macroeconomic variables when structuring their portfolios and diversification strategies. (iii) Policymakers should seek to minimize macroeconomic fluctuations considering the effect of macroeconomic variables changes on the stock market when formulating economic policy.

The 2007-2008 US subprime mortgage crisis evolved into a financial crisis that negatively affected many economies in the world and therefore it was widely referred to as the global financial crisis. Since the beginning of this financial crisis of 2008-2009, South Africa experienced a significant increase in its household debt to income ratio. In the main, the aim of this dissertation is to investigate the prominent factors contributing to the rise in the level of household debt in South Africa. Also, we study the response of household debt to various shocks originating from the aforementioned crisis. Additionally, in the context of our timeline (1985 Q1-2012 Q1) we will extrapolate possible graphical trends in the rise and fall of household indebtedness in South Africa associated with various crises. Working from past research papers and a theoretical framework developed by Franco Modigliani and Milton Friedman, seven macroeconomic variables will be considered to examine the rise of household borrowing to income namely; the real house price index, consumer price index. real income, real prime rate, real household consumption expenditure, real gross domestic product and real household savings. Both a long-run cointegration analysis and a short-run error correction model will be used to evaluate the relationship between household debt and the chosen variables by estimating a Vector Error Correction Model. Furthermore, the Variance Decomposition and the Generalized Impulse Response Function will be utilized to assess the impact of household debt to various shocks emanating from the 2008-2009 financial crisis. The different models and tests conducted in this research will be executed using the statistical software package EVIEWS 7. Based on the results, household debt was seen to have been fairly affected by the 2008-2009 financial crisis. The cointegration analysis maintains that in the long run, household borrowing is positively and significantly determined by consumer price index and real household consumption. In addition, it confirms that household borrowing is negatively affected by real household income and real GOP. The rest of the variables were found insignificant. Nevertheless, the short run error correction model reveals that about 3.6% of the disequilibrium will be corrected each quarter for the equilibrium state to be restored. Also, the Variance Decomposition results confirmed that the South African household debt is mostly affected by shocks from real house price index, real household income, real household consumption and real household savings, respectively. Furthermore, the Generalized Impulse Response Function results established the significant positive response of household debt to a shock from real house price index and real household consumption. The response of debt to shocks from consumer price index, real household savings and real income is negative and this outcome is confirmed by the theory. However, the response of debt shows fluctuating behaviours to shocks from LRIN, LRPR and LRGDP over the estimated period. In conclusion, our econometric investigation highlighted the main causes of the high levels of household debt in South Africa both in the short and long run. The Generalized Impulse Response Functions confirm that shocks like the occurrence of the 2007-2008 financial crisis will have a significant impact on real house price index, consumer price index, real household consumption and real household savings. The Engle granger results show that there exist no significant relationship between household debt and unemployment in South Africa over the period 1980 to 2010. However, we propose that this result may have been significant if quarterly unemployment data was available and included in the main data set. Finally, based on the stability, validity and reliability of our model, we recommend its use to facilitate policy analysis and decision making regarding household debt levels in South Africa. / Thesis (M.Com.( Economics) North-West University, Mafikeng Campus, 2012

Foreign trade is increasingly becoming a powerful tool when it comes to the promotion of economic growth in modern economies. This is especially so in the face of the continued rise of globalisation. In consideration of this fact, this thesis assessed the impact of foreign trade on the growth process of Namibia’s economy for the period stretching from 1990 to 2012. This main objective was further developed into primary, theoretical and empirical objectives. In order to realise these multiple objectives, two modern econometric time series techniques were employed, namely vector autoregressive (VAR) and auto-regression distributed lag (ARDL) models. Based on these two techniques, the following procedures featured during the study: Stationary tests, error correction modelling, co-integration tests, Granger causality tests, generalised impulse response functions and generalised forecast error variance decomposition. The following constitutes the main findings arising from this study: First, the study found that there is a positive relationship among the variables that were investigated. Indeed, this positive relationship suggests that the economy of Namibia can be expanded potentially by means of foreign trade. The result is also in line with economic theory. Secondly, the empirical findings also show that export, foreign direct investment and exchange rate endogenously respond to shocks in economic growth. Thirdly, economic growth itself accounted for most of the innovations that occurred during the period under consideration concerning economic growth. Fourthly, amongst the three explanatory variables used in the model, exports and foreign direct investment contributed more towards innovations in economic growth during the forecast period. Initially, exports and foreign direct investment dominated over the forecast horizon with each contributing almost an equal share of over 5 percent after 12 quarters. Thereafter, exports’ contribution relatively exceeded that of foreign direct investment. Fifthly, it is particularly important to note that the exchange rate variable made the weakest contribution towards explaining economic growth for the forecast period of 24 quarters. In consideration of the general constraints associated with this study, the thesis puts forward a number of proposals for possible further investigation by any theorist who is keen about probing the issue that the thesis investigated. The thesis considers the following as its significant contributions to the existing literature: First, this study primarily examined the relationship between exports and economic growth. By adding the effect of foreign direct investment and exchange rate to the analysis, this study became more comprehensive. This further widens the scope for policymaking for Namibia, as well as other developing economies on a similar route. Secondly, the study employed two modern econometric time series techniques, namely VAR and ARDL models in investigating the research topic under consideration. Most of the related studies that were reviewed either utilised ordinary least squares (OLS) or VAR or ARDL approach on its own. By implication, the results obtained from this study, therefore, are from a technical point of view more robust. Thirdly, through constructive comments, this thesis made valuable contributions to the relevant empirical literature as reviewed during the course of the study. Fourthly, since this study has a focus on Namibia, it provided the opportunity for the thesis to present a comprehensive analysis on issues pertaining to Namibia specifically. Lastly, the various recommendations put forward by this thesis will assist Namibia, as well as other developing countries, on a related path when it comes to formulating policies for the promotion of exports in particular and economic growth in general. / PhD (Economics)--North-West University, Vaal Triangle Campus, 2015.

Foreign trade is increasingly becoming a powerful tool when it comes to the promotion of economic growth in modern economies. This is especially so in the face of the continued rise of globalisation. In consideration of this fact, this thesis assessed the impact of foreign trade on the growth process of Namibia’s economy for the period stretching from 1990 to 2012. This main objective was further developed into primary, theoretical and empirical objectives. In order to realise these multiple objectives, two modern econometric time series techniques were employed, namely vector autoregressive (VAR) and auto-regression distributed lag (ARDL) models. Based on these two techniques, the following procedures featured during the study: Stationary tests, error correction modelling, co-integration tests, Granger causality tests, generalised impulse response functions and generalised forecast error variance decomposition. The following constitutes the main findings arising from this study: First, the study found that there is a positive relationship among the variables that were investigated. Indeed, this positive relationship suggests that the economy of Namibia can be expanded potentially by means of foreign trade. The result is also in line with economic theory. Secondly, the empirical findings also show that export, foreign direct investment and exchange rate endogenously respond to shocks in economic growth. Thirdly, economic growth itself accounted for most of the innovations that occurred during the period under consideration concerning economic growth. Fourthly, amongst the three explanatory variables used in the model, exports and foreign direct investment contributed more towards innovations in economic growth during the forecast period. Initially, exports and foreign direct investment dominated over the forecast horizon with each contributing almost an equal share of over 5 percent after 12 quarters. Thereafter, exports’ contribution relatively exceeded that of foreign direct investment. Fifthly, it is particularly important to note that the exchange rate variable made the weakest contribution towards explaining economic growth for the forecast period of 24 quarters. In consideration of the general constraints associated with this study, the thesis puts forward a number of proposals for possible further investigation by any theorist who is keen about probing the issue that the thesis investigated. The thesis considers the following as its significant contributions to the existing literature: First, this study primarily examined the relationship between exports and economic growth. By adding the effect of foreign direct investment and exchange rate to the analysis, this study became more comprehensive. This further widens the scope for policymaking for Namibia, as well as other developing economies on a similar route. Secondly, the study employed two modern econometric time series techniques, namely VAR and ARDL models in investigating the research topic under consideration. Most of the related studies that were reviewed either utilised ordinary least squares (OLS) or VAR or ARDL approach on its own. By implication, the results obtained from this study, therefore, are from a technical point of view more robust. Thirdly, through constructive comments, this thesis made valuable contributions to the relevant empirical literature as reviewed during the course of the study. Fourthly, since this study has a focus on Namibia, it provided the opportunity for the thesis to present a comprehensive analysis on issues pertaining to Namibia specifically. Lastly, the various recommendations put forward by this thesis will assist Namibia, as well as other developing countries, on a related path when it comes to formulating policies for the promotion of exports in particular and economic growth in general. / PhD (Economics)--North-West University, Vaal Triangle Campus, 2015.

This paper offers a re-assessment of the finance-growth nexus in a framework that allows to distinguish between short-run versus long-run effects. Our dataset contains information on 45 developed and developing countries over the period 1995-2011. We make use of the integration and cointegration properties of the data, establish a cointegrating relation and derive the long-run elasticities of per capita GDP with respect to employment, the physical capital stock, and financial development. We employ these results to specify an error correction model and assess whether the years of crisis have changed the relationship between finance and growth. (author's abstract) / Series: Department of Economics Working Paper Series

隨著台灣股票市場的自由化與國際化，信用交易與外資在台股的交易比重不斷的增加。本文旨在探討股價指數、信用交易指標之融資餘額與外資之關連性，利用Johansen共整合向量分析與誤差修正模型，以日資料進行實證分析研究，樣本期間為1998年1月2日起自2003年6月30日止，共1419個樣本觀測值。本研究結果如下：一、第t期的融資餘額與第t-2期的股價指數共整合程度最高，顯示股價指數領先融資餘額兩期，為其領先指標。二、同期的股價指數與外資持股共整合程度最高，且股價指數會受到前一期外資持股變量的影響，顯示外資在市場上的動作的確會造成其他投資人的跟進。三、同期的融資餘額與外資持股共整合程度最高，顯示兩者呈現同方向的變動，且外資持股會受到融資餘額前一期變量的影響，且方向相反。 / This paper examines the relationship between stock index, balance of margin trading, and stock holding of foreign investors. Using daily data from January 2 1998 through June 30 2003 we investigate the interactions among the three variables through Johansen cointegration analysis and error correction model. It is found that (1) balance of margin trading of time t and stock index of time t-2 have the highest level of cointegration, which means stock index leads the balance of margin trading for two days. (2) stock index and stock holding of foreign investors of the same time t have the highest level of cointegration, and stock index of time t is affected by the stock holding of foreign investors of time t-1. (3) balance of margin trading and stock holding of the same time t have the highest level of cointegration, and the stock holding of foreign investors at time t is adversely influenced by balance of margin trading of time t-1.

金融自由化後，金融商品交易的多樣性在活絡金融市場方面佔有很重的份量，也使得投資者有更多樣化的投資管道及標地。投資者購買金融商品除了追求較高的報酬外，對於投資風險的管理也是不容乎視。2007年，美國的次級房貸subprimemortgage風爆使得雷曼兄弟和AIG集團爆發財務危機，正是投資者追求高報酬之後，在風險管理上並未妥善管理所造成。 　　 　　衡量風險時，通常會使用變異數或標準差當做衡量指標，即在衡量其波動性，因此波動性裏含有許多訊息。在本論文中，我們將探討波動性所透露出來的兩個訊息，一個是風險值(VaR)，文中將分別使用二種衡量可解釋長期記憶的GARCH模型探討台股指數期貨及新加坡的摩台股指數期貨這兩個期貨市場的VaR。另外則是試圖尋找出這兩個期貨市場殘差值的波動性之間的長期共整合關係。 本論文主要由三篇文章組成，第一篇是利用Baillie, Bollerslev, and Millelsen (1996) 所提出的長期記憶模型FIGARCH來計算台指期貨的風險值（VaR）；第二篇也是利用長期記憶模型來計算新加坡的摩台指期貨的風險值，但這次的長期記憶模型增加一個由Tse (1998)　提出的可以考慮不對稱性波動的FIAPARCH模型。 　　這兩個模型都搭配三種不同的分配來計算VaR，分別是Normal, Student-t和skewed Student-t分配；實證結果顯示，這兩個期貨市場報酬的波動皆具有長期記憶，表示之前影響指數期貨報酬率的因素對未來指數期貨報酬率會有較長時間的影響力。而在傳統認為差殘值服從常態分配的假定下所計算出的VaR的配適情況較以Student-t分配計算出的VaR的配適情況不具效率，這除了說明傳統的常態分配假說在計算此兩個指數期貨報酬率是不適用之外，亦得出他們是具有肥尾（厚尾）的現象。 　　第三篇則是結合前兩篇的結果來探討此兩個指數期貨報酬率之間的波動性是否具有長期關係。因為台指期貨報酬率與摩台指期貨報酬率的波動性皆具有長期記憶，故在此部分，利用Engle-Granger (1987) 的兩階段共整合模型來求此兩個指數期貨報酬率之間的波動性是否存在長期關係。實證結果顯示，他們確實存在長期共整合關係，且摩台指期貨報酬率的波動性較台指期貨報酬率的波動性強，因此我們可以在台指期貨市場買入期指，而在新加坡的摩台指期貨市場避險 / The finance commodity exchange's multiplicity holds the very heavy component in the detachable money market aspect, after the financial liberalization. It also enables the investor to have many chances and commodities of investment. The investor purchases the financial commodity besides the higher reward, and does not allow regarding investment risk's management to regard. In 2007, the securitization commodity violation of US's subprimemortgage explodes causes Lehman Brothers and the AIG group erupts the financial crisis. This is precisely the investor pursues the high reward, and their administration centers have not created properly in the risk management. When we measure risks, we usually adopt the variance or the standard deviation. That is to weight its property of volatilities. There is much information in the volatilities. In this thesis, we discussed two kinds of information which the property of volatilities discloses. One is the value at risk (VaR hereafter). In this article, we use long-term memory's GARCH model to explain that the VaR of Taiwan stock index futures returns and Singapore's MSCI Taiwan index futures returns. Moreover, we attempts to seek for whether there are long relationship of the residuals volatilities between these two futures markets. This thesis was combined by three essays. The first essay employed the FIGARCH model of Baillie, Bollerslev, and Millelsen (1996) to calculated the VaR of Taiwan stock index futures returns. The second essay employed the FIGARCH model and FIAPARCH model of Tse (1998) to calculated the VaR of Singapore's MSCI Taiwan index futures returns. We calculated the VaRs of the different two futures markets by using the FIGARCH and FIAPARCH models with three different distributions-normal, student-t and skewed student-t. The empirical results showed the two futures markets both has long memory. It is not efficient to calculated the VaRs by using the traditional normal distribution. The Student-t distribution fitted the model better than the normal distribution. The third essay, we employed the Engle-Granger (1987) two-step cointegration model to test whether there are long relationship of the residuals volatilities between the Taiwan stock index futures returns and Singapore's MSCI Taiwan index futures returns. The empirical results showed that there was fractional cointegration between the two futures markets and the volatility in Taiwan stock index futures market is about 83% of that in MSCI Taiwan Index Futures market.