Immeasurable effort has been dedicated to estimating mortality using direct and indirect demographic techniques. However, literature available on methods applied to replacing missing values for non-responses in surveys or censuses so that these methods are implemented using sound data is sparse. The National Income and Dynamics Study (NIDS) household dataset includes the relationship of the deceased to the head of household variable. The relationship of the deceased to the head of household and the age of the head of household are incorporated into the Multiple Imputation (MI) technique proposed by Rubin (1987) to impute the missing ages at death for the deceased.

The United Nations Population Division publishes fertility projections for all countries in the World Population Prospects (WPP). These are the most widely used projections for planning and policy implementation. Despite a substantial body of literature that suggests education has a significant impact on fertility, these projections do not incorporate changes in the composition of the population by level of education. We therefore propose and implement a method that incorporates education composition change in projecting fertility. We investigate fertility differentials by level of education, then evaluate how education influences fertility independently; and finally, a model is fitted to project fertility rates by education levels. In both cases, the fertility rates by education level are then weighted by the IIASA educational attainment distributions to get the national fertility rates. These national fertility rates are in turn validated against the WPP fertility rates to evaluate how good the proposed method works. Fertility is high among the less educated relative to educated women. Education proves to be an important driver of fertility decline in Southern Africa. The proposed model is a good fit for countries with sufficient DHS data. However, there are other sources of data that are available, for example, the census data but we could not rely on them since they only give summary information. Validation was done to evaluate how good the model is working. This exercise produced consistent results with the observed fertility estimates. The percentage difference between the projected and WPP fertility estimates varied from 1 to 5 percent in Lesotho, Namibia and Zimbabwe. In conclusion, the model can also be used for other countries. Furthermore, education composition change should be considered when projecting fertility since it has proven to be a significant driver of fertility change. Data quality and availability issues were a major limitation to our study and in future should be improved.

Child mortality can be used to measure the level of social development as well as the health status of children (Hill 1991). By world regions, sub-Saharan Africa maintains the highest rates of under-five mortality. Current under-five mortality is estimated at 76 deaths per 1,000 live births (Hug, Sharrow, Zhong et al. 2018). In Zambia, under-five mortality reached a peak of 197 in 1996 and is currently estimated at 60 (Hug, Sharrow, Zhong et al. 2018). On the world health agenda, reducing child mortality has been made a priority, especially for low income countries that remain the most affected. Among the targets of the Sustainable Development Goals (SDGs) is reduction of neonatal mortality to at least 12 deaths per 1,000 live births and under-five mortality to 25 deaths by 2030 (United Nations 2015). HIV/AIDS is one of the leading causes of mortality in Zambia and has contributed to the slow decline of under-five mortality (Garenne and Gakusi 2006). Children under the age of five years get infected with HIV mainly through vertical transmission (Fishel, Ren, Barrère et al. 2014). In the absence of treatment, vertical transmission of HIV is high and can range between 15 and 45 per cent, reducing below 5 per cent with effective interventions (Barral, Oliveira, Lobato et al. 2014). Despite vertical transmission being the main pathway through which children get infected with HIV, little research has been done to determine the significance of maternal HIV status on under-five mortality in Zambia. The aim of the study was, therefore, to determine the extent to which mortality of children with HIV-positive mothers differs from that of children with HIV-negative mothers. The Zambia Demographic and Health Survey (ZDHS) data for 2007 and 2014 which contain HIV serotesting data were used. Survival analysis using Poisson regression was used to model the influence of maternal HIV status taking into account confounding factors. The results of the study indicate that maternal HIV status was significantly associated with child mortality in both survey periods but by 2013/14 the influence of maternal HIV status had reduced and was insignificant for children born within one year of the 2013/14 survey. The reduction in the risk of dying between the inter-survey period may be as a result of increased coverage of prevention of mother-to-child transmission (PMTCT) and antiretroviral therapy (ART) services over the years. In order to reach universal coverage, there is need for increased provision of PMTCT and ART treatments and support for HIV strategies such as the 90 90 90 target.

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.