In this thesis we study three basic issues related to international black tea markets: Are black tea markets integrated? Where is the price of black tea discovered? Are there leaders and followers in black tea markets? We use two statistical techniques as engines of analysis. First, we use time series methods to capture regularities in time lags among price series. Second, we use directed acyclic graphs to discover how surprises (innovations) in prices from each market are communicated to other markets in contemporaneous time. Weekly time series data on black tea prices from seven markets around the world are studied using time series methods. The study follows two paths. We study these prices in a common currency, the US dollar. We also study prices in each country's local currency. Results from unit root tests suggest that prices from three Indian markets are not generated through random walk-like behavior. We conclude that the Indian markets are not weak form efficient. However, prices from all non-Indian markets cannot be distinguished from random walk-like behavior. These latter markets are weak form efficient. Further analysis on these latter markets is conducted to determine whether information among the markets is shared. Vector Autoregressions (VARs) on the non-Indian markets are studied using directed acyclic graphs, impulse response functions and forecast error decomposition analyses. In both local currencies and dollar-converted series, the Sri Lankan and Indonesian markets are price leaders in contemporaneous time. Kenya is an information sink. It is endogenous in current time. Malawi is an exogenous price leader in dollar terms, but it is endogenous in local currency in contemporaneous time. In the long run, Sri Lanka, Indonesia and Malawi are price leaders in US dollar terms. In local currency series, Indonesia, Kenya and Malawi are price leaders in the long run. We use Theil's U-statistic to test the forecasting ability of the VAR models. We find for most markets in either dollars or on local currencies that a random walk forecast outperforms the VAR generated forecasts. This last result suggests the non-Indian markets are both weak form and semi-strong form efficient.

This research is based on a detailed description of model building for multivariate time series models. Under the assumption of stationarity, identification, estimation of the parameters and diagnostic checking for the Vector Auto regressive (p) (VAR(p)), Vector Moving Average (q) (VMA(q)) and Vector Auto regressive Moving Average (VARMA(p, q) ) models are described in detail. With reference to the non-stationary case, the concept of cointegration is explained. Procedures for testing for cointegration, determining the cointegrating rank and estimation of the cointegrated model in the VAR(p) and VARMA(p, q) cases are discussed. The utility of multivariate time series models in the field of economics is discussed and its use is demonstrated by analysing quarterly South African inflation and wage data from April 1996 to December 2008. A review of the literature shows that multivariate time series analysis allows the researcher to: (i) understand phenomenon which occur regularly over a period of time (ii) determine interdependencies between series (iii) establish causal relationships between series and (iv) forecast future variables in a time series based on current and past values of that variable. South African wage and inflation data was analysed using SAS version 9.2. Stationary VAR and VARMA models were run. The model with the best fit was the VAR model as the forecasts were reliable, and the small values of the Portmanteau statistic indicated that the model had a good fit. The VARMA models by contrast, had large values of the Portmanteau statistic as well as unreliable forecasts and thus were found not to fit the data well. There is therefore good evidence to suggest that wage increases occur independently of inflation, and while inflation can be predicted from its past values, it is dependent on wages. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2012.

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The objective of this dissertation is to model the volatility of financial time series data using ARCH, GARCH and stochastic volatility models. It is found that the ARCH and GARCH models are easy to fit compared to the stochastic volatility models which present problems with respect to the distributional assumptions that need to be made. For this reason the ARCH and GARCH models remain more widely used than the stochastic volatility models. The ARCH, GARCH and stochastic volatility models are fitted to four data sets consisting of daily closing prices of gold mining companies listed on the Johannesburg stock exchange. The companies are Anglo Gold Ashanti Ltd, DRD Gold Ltd, Gold Fields Ltd and Harmony Gold Mining Company Ltd. The best fitting ARCH and GARCH models are identified along with the best error distribution and then diagnostics are performed to ensure adequacy of the models. It was found throughout that the student-t distribution was the best error distribution to use for each data set. The results from the stochastic volatility models were in agreement with those obtained from the ARCH and GARCH models. The stochastic volatility models are, however, restricted to the form of an AR(1) process due to the complexities involved in fitting higher order models. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

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Traffic-related injuries represent a global public health problem, and contribute largely to mortality and years lived with disability worldwide. Over the course of the last decades, improvements to road traffic safety and injury surveillance systems have resulted in a shift in focus from the prevention of motor vehicle accidents to the control of injury events involving vulnerable road users (VRUs), such as cyclists and moped riders. There have been calls for improvements to the evaluation of safety interventions due to methodological problems associated with the most commonly used study designs. The purpose of this licentiate thesis was to assess the strengths and limitations of the interrupted time series (ITS) design, which has gained some attention for its ability to provide valid effect estimates. Two national road safety interventions involving VRUs were selected as cases: the Swedish bicycle helmet law for children under the age 15, and the tightening of licensing rules for Class 1 mopeds. The empirical results suggest that both interventions were effective in improving the safety of VRUs. Unless other concurrent events affect the treatment population at the exact time of intervention, the effect estimates should be internally valid. One of the main limitations of the study design is the inability to identify why the interventions were successful, especially if they are complex and multifaceted. A lack of reliable exposure data can also pose a further threat to studies of interventions involving VRUs if the intervention can affect the exposure itself. It may also be difficult to generalize the exact effect estimates to other regions and populations. Future studies should consider the use of the ITS design to enhance the internal validity of before-after measurements. / Traffic-related injuries represent a global public health problem, and contribute largely to mortality and years lived with disability. Over the course of the last decades, improvements to road traffic safety and injury surveillance systems have resulted in a shift in focus from motor vehicle accidents to injury events involving vulnerable road users (VRUs), such as cyclists and moped riders. There have been calls for improvements to the evaluation of safety interventions due to methodological problems associated with the most commonly used study designs. The purpose of this licentiate thesis was to assess the strengths and limitations of the interrupted time series (ITS) design, which has gained some attention for its ability to provide valid effect estimates while accounting for secular trends. Two national interventions involving VRUs were selected as cases: the Swedish bicycle helmet law for children under the age 15, and the tightening of licensing rules for Class 1 mopeds. The empirical results suggest that both interventions were effective. These results are discussed in the light of some methodological considerations regarding internal and external validity, data quality and the ability to fully understand key causal mechanisms behind complex interventions.

Saudi Arabia is the largest petroleum producer and exporter in the world. Saudi Arabian economy hugely depends on production and export of oil. This motivates us to do research on oil production of Saudi Arabia. In our research the prime objective is to find the most appropriate models for analyzing Saudi Arabia oil production data. Initially we think of considering integrated autoregressive moving average (ARIMA) models to fit the data. But most of the variables under study show some kind of volatility and for this reason we finally decide to consider autoregressive conditional heteroscedastic (ARCH) models for them. If there is no ARCH effect, it will automatically become an ARIMA model. But the existence of missing values for almost each of the variable makes the analysis part complicated since the estimation of parameters in an ARCH model does not converge when observations are missing. As a remedy to this problem we estimate missing observations first. We employ the expectation maximization (EM) algorithm for estimating the missing values. But since our data are time series data, any simple EM algorithm is not appropriate for them. There is also evidence of the presence of outliers in the data. Therefore we finally employ robust regression least trimmed squares (LTS) based EM algorithm to estimate the missing values. After the estimation of missing values we employ the White test to select the most appropriate ARCH models for all sixteen variables under study. Normality test on resulting residuals is performed for each of the variable to check the validity of the fitted model. / ARCH/GARCH models, outliers and robustness : tests for normality and estimation of missing values in time series -- Outlier analysis and estimation of missing values by robust EM algorithm for Saudi Arabia oil production data -- Selection of ARCH models for Saudi Arabia oil production data. / Department of Mathematical Sciences