Short-term hourly load forecasting in South Africa using additive quantile regression (AQR) models is discussed in this study. The modelling approach allows for easy interpretability and accounting for residual autocorrelation in the joint modelling of hourly electricity data. A comparative analysis is done using generalised additive models (GAMs). In both modelling frameworks, variable selection is done using least absolute shrinkage and selection operator (Lasso) via hierarchical interactions. Four models considered are GAMs and AQR models with and without interactions, respectively. The AQR model with pairwise interactions was found to be the best fitting model. The forecasts from the four models were then combined using an algorithm based on the pinball loss (convex combination model) and also using quantile regression averaging (QRA). The AQR model with interactions was then compared with the convex combination and QRA models and the QRA model gave the most accurate forecasts. Except for the AQR model with interactions, the other two models (convex combination model and QRA model) gave prediction interval coverage probabilities that were valid for the $90\%$ , $95\%$ and the $99\%$ prediction intervals. The QRA model had the smallest prediction interval normalised average width and prediction interval normalised average deviation. The modelling framework discussed in this paper has established that going beyond summary performance statistics in forecasting has merit as it gives more insight into the developed forecasting models.

Background: South Africa has a high burden of tuberculosis (TB) disease and is currently not meeting the national and international reduction outcome targets. The TB prevalence rate of South Africa in 2015 was estimated at approximately 690 per 100,000 population per year, with an incidence rate of about 834 per 100,000 population. This study examines risk factors associated with development of TB in South Africa. Materials and Methods: This study utilised readily available open access secondary data of 2019 South African Health and Demographic Survey from Statistics South Africa (StatsSA) website, which was collected from self-reported information relating to TB in the household questionnaire. The factors analysed were of demographic, socio-economic and health nature. Bivariate and binary logistics analyses were carried out from which appropriate inferences were drawn on the association of TB with demographic, socio-economic and health factors. Results: In multivariate analysis the study revealed that age, personal weight, smoke, alcohol, asthma, province of residence, race and usually coughing were significantly associated with an increased risk of having TB. Conclusions and Recommendations: The results strongly suggest that young and older people coming from black and coloured ethic groups, who are asthmatic and cough frequently, and/or smoking and consuming alcohol are at high risk of developing TB. In addition, those who are overweight appear to have an increased risk of TB transmission, with the Western Cape, Eastern Cape, Northern Cape, Free State, North West and Gauteng being the hardest hit provinces. Hence, the study recommends that these factors must be taken into account in the planning and development of TB policies in order to work successfully towards the achievement of sustainable development goal of reducing TB by 80% before 2030.

The S&P 500 Index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past few years, Bitcoin has grown in popularity and adoption. This study analyzes the daily return distribution of Bitcoin and the S&P 500 Index and assesses their tail probabilities using two financial risk measures. As a methodology, we use Bitcoin and S&P 500 Index daily return data to fit the seven-parameter General Tempered Stable (GTS) distribution using the advanced fast fractional Fourier transform (FRFT) scheme developed by combining the fast fractional Fourier transform algorithm and the 12-point composite Newton–Cotes rule. The findings show that peakedness is the main characteristic of the S&P 500 Index return distribution, whereas heavy-tailedness is the main characteristic of Bitcoin return distribution. The GTS distribution shows that $80.05\%$ of S&P 500 returns are within $-1.06\%$ and $1.23\%$ against only $40.32\%$ of Bitcoin returns. At a risk level ($\alpha$), the severity of the loss ($AVa{R}_{\alpha }\left(X\right)$) on the left side of the distribution is larger than the severity of the profit ($AVa{R}_{1-\alpha }\left(X\right)$) on the right side of the distribution. Compared to the S&P 500 Index, Bitcoin has $39.73\%$ more prevalence to produce high daily returns (more than $1.23\%$ or less than $-1.06\%$). The severity analysis shows that, at $\alpha$ risk level, the average value-at-risk ($AVaR\left(X\right)$) of Bitcoin returns at one significant figure is four times larger than that of the S&P 500 Index returns at the same risk.

In this article we fit a time-dependent generalised extreme value (GEV) distribution to annual maximum flood heights at three sites: Chokwe, Sicacate and Combomune in the lower Limpopo River basin of Mozambique. A GEV distribution is fitted to six annual maximum time series models at each site, namely: annual daily maximum (AM1), annual 2-day maximum (AM2), annual 5-day maximum (AM5), annual 7-day maximum (AM7), annual 10-day maximum (AM10) and annual 30-day maximum (AM30). Non-stationary time-dependent GEV models with a linear trend in location and scale parameters are considered in this study. The results show lack of sufficient evidence to indicate a linear trend in the location parameter at all three sites. On the other hand, the findings in this study reveal strong evidence of the existence of a linear trend in the scale parameter at Combomune and Sicacate, whilst the scale parameter had no significant linear trend at Chokwe. Further investigation in this study also reveals that the location parameter at Sicacate can be modelled by a nonlinear quadratic trend; however, the complexity of the overall model is not worthwhile in fit over a time-homogeneous model. This study shows the importance of extending the time-homogeneous GEV model to incorporate climate change factors such as trend in the lower Limpopo River basin, particularly in this era of global warming and a changing climate.

Extreme rainfall events have made significant damages to properties, public infrastructure and agriculture in some provinces of South Africa notably in KwaZulu-Natal and Gauteng among others. The general global increase in the frequency and intensity of extreme precipitation events in recent years is raising a concern that human activities might be heavily disturbed. This study attempts to model long-term monthly rainfall variability in the selected provinces of South Africa using various statistical techniques. The study investigates the normality and stationarity of the underlying distribution of the whole body of rainfall data for each selected province, the long-term trends of the rainfall data and the extreme value distributions which model the tails of the rainfall distribution data. These approaches were meant to help achieve the broader purpose of this study of investigating the long-term rainfall trends, stationarity of the rainfall distributions and extreme value distributions of monthly rainfall records in the selected provinces of South Africa in this era of climate change. The five provinces considered in this study are Eastern Cape, Gauteng, KwaZulu-Natal, Limpopo and Mpumalanga. The findings revealed that the long-term rainfall distribution for all the selected provinces does not come from a normal distribution. Furthermore, the monthly rainfall data distribution for the majority of the provinces is not stationary. The paper discusses the modelling of monthly rainfall extremes using the non-stationary generalised extreme value distribution (GEVD) which falls under the block maxima extreme value theory (EVT) approach. The maximum likelihood estimation method was used to obtain the estimates of the parameters. The stationary GEVD was found as the best distribution model for Eastern Cape, Gauteng, and KwaZulu-Natal provinces. Furthermore, model fitting supported non-stationary GEVD model for maximum monthly rainfall with nonlinear quadratic trend in the location parameter and a linear trend in the scale parameter for Limpopo, while in Mpumalanga the non-stationary GEVD model with a nonlinear quadratic trend in the scale parameter and no variation in the location parameter fitted well to the monthly rainfall data. The negative values of the shape parameters for Eastern Cape and Mpumalanga suggest that the data follow the Weibull distribution class, while the positive values of the shape parameters for Gauteng, KwaZulu-Natal and Limpopo suggest that the data follow the Fréchet distribution class. The findings from this paper could give information that can assist decision makers establish strategies for proper planning of agriculture, infrastructure, drainage system and other water resource applications in the South African provinces.