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Item Financial modelling of cryptocurrency: a case study of Bitcoin, Ethereum, and Dogecoin in comparison with JSE stock returns.(2022) Kaseke, Forbes.; Ramroop, Shaun.; Mwambi, Henry Godwell.The emergency of cryptocurrency has caused a shift in the financial markets. Although it was created as a currency for exchange, cryptocurrency has been shown to be an asset, with investors seeking to profit from it rather than using it as a medium of exchange. Despite being a financial asset, cryptocurrency has distinct, stylised facts like any other asset. Studying these stylised facts allows the creation of better-suited models to assist investors in making better data-driven decisions. The data used in this thesis was of three leading cryptocurrencies: Bitcoin, Ethereum, and Dogecoin and the Johannesburg Stock Exchange (JSE) data as a guide for comparison. The sample period was from 18 September 2017 to 27 May 2021. The goal was to research the stylised facts of cryptocurrencies and then create models that capture these stylised facts. The study developed risk-quantifying models for cryptocurrencies. The main findings were that cryptocurrency exhibits stylised facts that are well-known in financial data. However, the magnitude and frequency of these stylised facts tend to differ. For example, cryptocurrency is more volatile than stock returns. The volatility also tends to be more persistent than in stocks. The study also finds that cryptocurrency has a reverse leverage effect as opposed to the normal one, where past negative returns increase volatility more than past positive returns. The study also developed a hybrid GARCH model using the extreme value theorem for quantifying cryptocurrency risk. The results showed that the GJR-GARCH with GDP innovations could be used as an alternative model to calculate the VaR. The volatile nature of cryptocurrency was also compared with that of the JSE while accounting for structural breaks and while not accounting for them. The results showed that the cryptocurrencies’ volatility patterns are similar but differ from those of the JSE. The cryptocurrency was also found to be an inefficient market. This finding means that some investors can take advantage of this inefficiency. The study also revealed that structural breaks affect volatility persistence. However, this persistence measure differs depending on the model used. Markov switching GARCH models were used to strengthen the structural break findings. The results showed that two-regime models outperform single-regime models. The VAR and DCC-GARCH models were also used to test the spillovers amongst the assets used. The results showed short-run spillovers from Bitcoin to Ethereum and long-run spillovers based on the DCC-GARCH. Lastly, factors affecting cryptocurrency adoption were discussed. The main reasons affecting mass adoption are the complexity that comes with the use of cryptocurrency and its high volatility. This study was critical as it gives investors an understanding of the nature and behaviour of cryptocurrency so that they know when and how to invest. It also helps policymakers and financial institutions decide how to treat or use cryptocurrency within the economy.Item Flexible Bayesian hierarchical spatial modeling in disease mapping.(2022) Ayalew, Kassahun Abere.; Manda, Samuel.The Gaussian Intrinsic Conditional Autoregressive (ICAR) spatial model, which usually has two components, namely an ICAR for spatial smoothing and standard random effects for non-spatial heterogeneity, is used to estimate spatial distributions of disease risks. The normality assumption in this model may not always be correct and misspecification of the distribution of random effects could result in biased estimation of the spatial distribution of disease risk, which could lead to misleading conclusions and policy recommendations. Limited research studies have been done where the estimation of the spatial distributions of diseases under the ICAR-normal model were compared to those obtained from fitting ICAR-nonnormal model. The results from these studies indicated that the ICAR-nonnormal models performed better than the ICAR-normal in terms of accuracy, efficiency and predictive capacity. However, these efforts have not fully addressed the effect on the estimation of spatial distributions under flexible specification of ICAR models in disease mapping. The overall aim of this PhD thesis was to develop approaches that relax the normality assumption that is often used in modeling and fitting of ICAR models in the estimation of spatial patterns of diseases. In particular, the thesis considered the skewnormal and skew-Laplace distributions under the univariate, and skew-normal for the multivariate specifications to estimate the spatial distributions of either univariable or multivariable areal data. The thesis also considered non-parametric specification of the multivariate spatial effects in the ICAR model, which is a novel extension of an earlier work. The estimation of the models was done using Bayesian statistical approaches. The performances of our suggested alternatives to the ICAR-normal model were evaluated by simulating studies as well as with practical application to the estimation of district-level distribution of HIV prevalence and treatment coverage using health survey data in South Africa. Results from the simulation studies and analysis of real data demonstrated that our approaches performed better in the prediction of spatial distributions for univariable and multivariable areal data in disease mapping approaches. This PhD has shown the limitations of relying on the ICAR-normal model for the estimations of spatial distributions for all spatial analyses, even when the data could be asymmetric and non-normal. In such scenarios, skewed-ICAR and nonparametric ICAR approaches could provide better and unbiased estimation of the spatial pattern of diseases.Item Statistical study on childhood malnutrition and anaemia in Angola, Malawi and Senegal.(2023) Khulu, Mthobisi Christian.; Ramroop, Shaun.; Habyarimana, Faustin.Malnutrition and anaemia continue to be a concern to the future of developing countries. This thesis aimed to examine the risk factors associated with malnutrition and anaemia among under five-year-old children in Angola, Malawi and Senegal. Statistical models and techniques have improved over the years to give more insight into malnutrition and anaemia, in terms of demographic, socio-economic, environmental, and geographic factors. This thesis also assessed the spatial epidemiological overlaps between childhood malnutrition and anaemia diseases which can lead to various advantages in intervention planning, monitoring, controlling and total elimination of such diseases, especially in high-risk regions. This is a secondary data analysis where national representative data from the three countries was used. The Demographic and Health Survey data from Angola, Malawi and Senegal were merged to create a pooled sample which was then used for all the analyses conducted in this study. The relationship between exploratory variables to malnutrition and anaemia was assessed to obtain variables that explain the two outcomes. Consequently, a generalized linear mixed model was used to investigate the significance of the child-level, community-level and household-level factors to malnutrition and anaemia separately. The relationship between the two diseases was further examined using the three joint modelling approaches: (1) a joint generalised linear mixed model; (2) a structural equation model, and (3) a bivariate copula geo-additive model. For each model employed, the significant factors of both malnutrition and anaemia were identified. The GLMM results on malnutrition revealed that children’s place of residence, age, gender, mother’s level of schooling, wealth status, birth interval and birth order significantly explain malnutrition at the 5% level of significance. Whereas, the GLMM results on anaemia revealed that children‘s age, gender, mother’s level of schooling, wealth status and nutritional status significantly explain anaemia at 5% level of significance. The findings of copula geo-additive modelling of malnutrition and anaemia indicated that there is an association between malnutrition and anaemia. There was a strong association observed between malnutrition and anaemia in the north-west districts of Angola when compared to other districts. The results imply that the policymakers of Angola, Senegal and Malawi can control anaemia through the intervention of malnutrition controlling. The overall findings of this study provide meaningful insight to the policymakers of Angola, Malawi and Senegal which will lead to the implementation of interventions that can assist in achieving the Sustainable Development Goal (SDG) of 25 deaths per 1 000 live births by 2030. To properly eradicate all the causes of malnutrition and anaemia, programs such as parental education, financial education, children's dietary focus programs and mobile health facilities could add a significant value. The results also highlighted the national priority areas related to child-related factors, household factors and environmental factors for childhood malnutrition and anaemia morbidity control. It also provided policy makers with valuable geographical information for developing and implementing effective intervention. There is a greater need for partnership and collaboration among the studied countries to achieve the SGD target.