We modelled the mean annual rainfall for data recorded in Zimbabwe from 1901 to 2009. Extreme value theory was used to estimate the probabilities of meteorological droughts. Droughts can be viewed as extreme events which go beyond and/or below normal rainfall occurrences, such as exceptionally low mean annual rainfall. The duality between the distribution of the minima and maxima was exploited and used to fit the generalised extreme value distribution (GEVD) to the data and hence find probabilities of extreme low levels of mean annual rainfall. The augmented Dickey Fuller test confirmed that rainfall data were stationary, while the normal quantile-quantile plot indicated that rainfall data deviated from the normality assumption at both ends of the tails of the distribution. The maximum likelihood estimation method and the Bayesian approach were used to find the parameters of the GEVD. The Kolmogorov–Smirnov and Anderson–Darling goodnessof- fit tests showed that the Weibull class of distributions was a good fit to the minima mean annual rainfall using the maximum likelihood estimation method. The mean return period estimate of a meteorological drought using the threshold value of mean annual rainfall of 473 mm was 8 years. This implies that if in the year there is a meteorological drought then another drought of the same intensity or greater is expected after 8 years. It is expected that the use of Bayesian inference may better quantify the level of uncertainty associated with the GEVD parameter estimates than with the maximum likelihood estimation method. The Markov chain Monte Carlo algorithm for the GEVD was applied to construct the model parameter estimates using the Bayesian approach. These findings are significant because results based on non-informative priors (Bayesian method) and the maximum likelihood method approach are expected to be similar.

Modelling the volatility of commodity prices and creating more reliable models for estimating and forecasting commodity price returns are crucial. The body of research on statistical models that can fully reflect the empirical characteristics of commodity price returns is lacking. The main aim of this research was to develop a modelling framework that could be used to accurately estimate and forecast commodity price returns by combining long memory models with heavy-tailed distributions. This study employed dual hybrid long-memory generalised autoregressive conditionally heteroscedasticity (GARCH) models with heavy-tailed innovations, namely, the Student-t distribution (StD), skewed-Student-t distribution (SStD), and the generalised error distribution (GED). Based on the smallest forecasting metrics values for mean absolute error (MAE) and mean squared error (MSE) values, the best performing LM-GARCH-type model for lithium is the ARFIMA (1, $\mathcal{o}$, 1)-FIAPARCH (1, $\xi$, 1) with normal innovations. For tobacco, the best model is ARFIMA (1, $\mathcal{o}$, 1)-FIGARCH (1, $\xi$, 1) with SStD innovations. The robust performing model for gold is the ARFIMA (1, $\mathcal{o}$, 1)-FIGARCH (1, $\xi$, 1)-GED model. The best performing forecasting model for crude oil and cotton returns are the $FIAPARCH \left(1,\xi , 1\right)-SStD$ model and $HYGARCH \left(1,\xi , 1\right)-StD$ model, respectively. The results obtained from this study would be beneficial to those concerned with financial market modelling techniques, such as derivative pricing, risk management, asset allocation, and valuation.

HIV remains a major public health challenge in sub-Saharan Africa, with South Africa bearing the highest burden. This study confirms that KwaZulu-Natal (KZN) is a hotspot, with a high HIV prevalence of 47.4% (95% CI: 45.7–49.1) among females aged 15–34. We investigated the spatial distribution and key socio-demographic, behavioural, and economic factors associated with HIV prevalence in this group using a Bayesian spatial logistic regression model. Secondary data from 3324 females in the HIV Incidence Provincial Surveillance System (HIPSS) (2014–2015) in uMgungundlovu District, KZN, were analysed. Bayesian spatial models fitted using the Integrated Nested Laplace Approximation (INLA) identified key predictors and spatial clusters of HIV prevalence. The results showed that age, education, marital status, income, alcohol use, condom use, and number of sexual partners significantly influenced HIV prevalence. Older age groups (20–34 years), alcohol use, multiple partners, and STI/TB diagnosis increased HIV risk, while tertiary education and condom use were protective. Two HIV hotspots were identified, with one near Greater Edendale being statistically significant. The findings highlight the need for targeted, context-specific interventions to reduce HIV transmission among young females in KZN.

This study is aimed at investigating the volatility dynamics and the risk-return relationship in the South African market, analyzing the FTSE/JSE All Share Index returns for an updated sample period of 2009–2019. The study employed several GARCH type models with different probability distributions governing the model’s innovations. Results have revealed strong persistent levels of volatility and a positive risk-return relationship in the South African market. Given the elaborate use of the GARCH approach of risk estimation in the existing finance literature, this study highlighted several weaknesses of the model. A noteworthy property of the GARCH approach was that the innovation distributions did not affect parameter estimation. Analyzing the GARCH type models, this theory was supported by the majority of the GARCH test results with respect to the volatility dynamics. On the contrary, it was strongly unsupported by the risk-return relationship. More specifically, it was found that while the innovations of the EGARCH (1, 1) model could account for the volatile nature of financial data, asymmetry remained uncaptured. As a result, misestimating of risks occurred, which could lead to inaccurate results. This study highlighted the significance of the innovation distribution of choice and recommended the exploration of different nonnormal innovation distributions to aid with capturing the asymmetry.

In this study, a multiple regression models developed to explain and predict mean annual rainfall in Zimbabwe. Principal component analysis is used to construct orthogonal climatic factors which influence rainfall patterns in Zimbabwe. The aim of the study is to develop a simple but reliable tool to predict annual rainfall one year in advance using Darwin Sea Level Pressure (Darwin SLP) value of a particular month and a component of Southern Oscillation Index (SOI) which is not explained by Darwin SLP. A weighted multiple regression approach is used to control for heteroscedasticity in the error terms. The model developed has a reasonable fit at the 5%statistical significance level can easily be used to predict mean annual rainfall at least a year in advance. DOI: 10.5901/mjss.2014.v5n7p34

South Africa’s economy has faced many downturns in the previous decade, and to curb the spread of the novel SARS-CoV-2, the lockdown brought South African financial markets to an abrupt halt. Therefore, the implementation of risk mitigation approaches is becoming a matter of urgency in volatile markets in these unprecedented times. In this study, a hybrid generalized autoregressive conditional heteroscedasticity (GARCH)-type model combined with heavy-tailed distributions, namely the Generalized Pareto Distribution (GPD) and the Nolan’s S0-parameterization stable distribution (SD), were fitted to the returns of three FTSE/JSE indices, namely All Share Index (ALSI), Banks Index and Mining Index, as well as the daily closing prices of the US dollar against the South African rand exchange rate (USD/ZAR exchange rate). VaR values were estimated and back-tested using the Kupiec likelihood ratio test. The results of this study show that for FTSE/JSE ALSI returns, the hybrid exponential GARCH (1,1) model with SD model (EGARCH(1,1)-SD) outperforms the GARCH-GPD model at the 2.5% VaR level. At VaR levels of 95% and 97.5%, the fitted GARCH (1,1)-SD model for FTSE/JSE Banks Index returns performs better than the GARCH (1,1)-GPD. The fitted GARCH (1,1)-SD model for FTSE/JSE Mining Index returns is better than the GARCH (1,1)-GPD at 5% and 97.5% VaR levels. Thus, this study suggests that the GARCH (1,1)-SD model is a good alternative to the VaR robust model for modeling financial returns. This study provides salient results for persons interested in reducing losses or obtaining a better understanding of the South African financial industry.