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Testing for purchasing power parity (PPP) and uncovered interest parity (UIP) has been the focus of many empirically oriented studies. While these simple economic theories of exchange rate and interest rate determination are theoretically attractive, the empirical support for these equilibrium conditions is at best mixed. Many potential reasons have been cited in the literature for the failure of such studies, ranging from market imperfections to inappropriate modelling strategies. The current state-of-the-art procedure involves testing for two cointegrating vectors in a multivariate error correction model which may be economically identified as the PPP and UIP relations. However, such a procedure does not account for policy regime shifts which distort the underlying PPP and UIP relations. In this paper, a Markov-switching vector error correction model (VECM) is considered for time series data in which monetary and exchange rate regime shifts are known to be present. Weak evidence in favour of PPP and UIP is established in a standard linear VECM, although the residuals of this model indicate that it is inappropriate in terms of functional form. The Markov-switching VECM, however, provides convincing evidence in favour of both the PPP and UIP relations and a marked improvement in the residual distributions.

The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φ_q-optimal designs. The approach is illustrated for two specific weighted polynomial models and also for a particular growth model.

For many problems of statistical inference in regression modelling, the Fisher information matrix depends on certain nuisance parameters which are unknown and which enter the model nonlinearly. A common strategy to deal with this problem within the context of design is to construct maximin optimal designs as those designs which maximize the minimum value of a real valued (standardized) function of the Fisher information matrix, where the minimum is taken over a specified range of the unknown parameters. The maximin criterion is not differentiable and the construction of the associated optimal designs is therefore difficult to achieve in practice. In the present paper the relationship between maximin optimal designs and a class of Bayesian optimal designs for which the associated criteria are differentiable is explored. In particular, a general methodology for determining maximin optimal designs is introduced based on the fact that in many cases these designs can be obtained as weak limits of appropriate Bayesian optimal designs.

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).