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.

The Journal of Economic and Financial Sciences promotes research in auditing, corporate finance, corporate governance, economics, econometrics, financial accounting, financial management, financial planning, investment management, management accounting and taxation in the emerging market field.

South Africa is a cornucopia of mineral riches and the performance of its mining industry has significant impacts on the economy. Hence, an accurate distributional assumption of the underlying mining index returns is imperative for the forecasting and understanding of the financial market. In this paper, we propose three subclasses of the generalized hyperbolic distributions as appropriate models for the Johannesburg Stock Exchange (JSE) Mining Index returns. These models are shown to outperform the traditional assumption of normality and accommodate for a number of stylized features, such as excess kurtosis and volatility clustering, embedded within the financial data. The models are compared using the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC) and log-likelihoods. In addition, Value-at-Risk (VaR) estimation and backtesting were also performed to test the extreme tails. The various criteria utilized suggest the generalized hyperbolic (GH) skew Students t-distribution as the most robust model for the South African Mining Index returns.

Extreme value theory (EVT) has been widely applied in fields such as hydrology and insurance. It is a tool used to reflect on probabilities associated with extreme, and thus rare, events. EVT is useful in modeling the impact of crashes or situations of extreme stress on investor portfolios. It describes the behavior of maxima or minima in a time series, i.e., tails of a distribution. In this paper, we propose the use of generalised Pareto distribution (GPD) to model extreme returns in the gold market. This method provides effective means of estimating tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). This is confirmed by various backtesting procedures. In particular, we utilize the Kupiec unconditional coverage test and the Christoffersen conditional coverage test for VaR backtesting, while the Bootstrap test is used for ES backtesting. The results indicate that GPD is superior to the traditional Gaussian and Students t models for VaR and ES estimations.

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.