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Includes abstract. Includes bibliographical references.

Kriging is a widely used group of techniques for predicting unobserved responses at specified locations using a set of observations obtained from known locations. Kriging predictors are best linear unbiased predictors (BLUPs) and the precision of predictions obtained from them are assessed by the mean squared prediction error (MSPE), commonly termed the kriging variance.

Includes bibliographical references (leaves 88-93)., This dissertation comprises a study into the application of count data time series models to weekly counts of cholera cases that have been recorded in Beira, Mozambique. The study specifically looks at two classes of time series models for count data, namely observation-driven and parameter-driven, and two models from each of these classes are investigated. The autoregressive conditional Poisson (ACP) and double autoregressive conditional Poisson (DACP) are considered under the observation-driven class, while the parameter-driven models used are the Poisson-gamma and stochastic autoregressive mean (SAM) model. An in-depth case study of the cholera counts is presented in which the four selected count data time series models are compared. In addition the time series models are compared to static Poisson and negative binomial regression, thereby indicating the benefits gained in using count data time series models when the counts exhibit serial correlation. In the process of comparing the models, the effect of environmental drivers on the outbreaks of cholera are observed and discussed.

The recent sub prime crisis has resulted in an increased focus on risk management and monitoring in the financial industry. One of the essential components of risk management and monitoring is a reliable ex-ante covariance matrix of various financial time series. Therefore a reliable model which can handle a large number of time series is required to calculate an ex-ante or conditional covariance matrix.

Includes bibliographical references (leaves 137-138)., This work investigates the modelling of non-stationary sample extremes using a roughness penalty approach, in which smoothed natural cubic splines are fitted to the location and scale parameters of the generalized extreme value distribution and the distribution of the r largest order statistics. Estimation is performed by implementing a Fisher scoring algorithm to maximize the penalized log-likelihood function. The approach provides a flexible framework for exploring smooth trends in sample extremes, with the benefit of balancing the trade-off between 'smoothness' and adherence to the underlying data by simply changing the smoothing parameter. To evaluate the overall performance of the extreme value theory methodology in smoothing extremes a simulation study was performed.

Includes abstract., Includes bibliographical references (leaves 100-101)., The aim of the study is to ascertain whether the information gained from the more complicated multivariate matrix decomposition models can be used to better forecast the covariance matrix and produce a Value at Risk estimate which more appropriately describes fat-tailed financial time-series.

Includes abstract. Includes bibliographical references (leaves [72]-75).

Includes bibliographical references (leaves 76-77).