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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.

Natural hazards (events that may cause actual disasters) are established in the literature as major causes of various massive and destructive problems worldwide. The occurrences of earthquakes, floods and heat waves affect millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. The focus of this study was on the risk reduction of the disasters that occur because of extremely high temperatures and heat waves. Modelling average maximum daily temperature (AMDT) guards against the disaster risk and may also help countries towards preparing for extreme heat. This study discusses the use of the r largest order statistics approach of extreme value theory towards modelling AMDT over the period of 11 years, that is, 2000–2010. A generalised extreme value distribution for r largest order statistics is fitted to the annual maxima. This is performed in an effort to study the behaviour of the r largest order statistics. The method of maximum likelihood is used in estimating the target parameters and the frequency of occurrences of the hottest days is assessed. The study presents a case study of South Africa in which the data for the non-winter season (September–April of each year) are used. The meteorological data used are the AMDT that are collected by the South African Weather Service and provided by Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for specified return periods are estimated using the quantile function and the best model is chosen through the use of the deviance statistic with the support of the graphical diagnostic tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit of the models to the data.

Weather and climate extremes such as heat waves, droughts and floods are projected to become more frequent and intense in several regions. There is compelling evidence indicating that changes in climate and its extremes over time influence the living conditions of society and the surrounding environment across the globe. This study applies max-stable models to capture the spatio–temporal extremes with dependence. The objective was to analyse the risk of drought caused by extremely high temperatures and deficient rainfall. Hopkin’s statistic was used to assess the clustering tendency before using the agglomerative method of hierarchical clustering to cluster the study area into n=3 temperature clusters and n=3 precipitation clusters. For the precipitation and temperature data, the values of Hopkin’s statistic were 0.7317 and 0.8446, respectively, which shows that both are significantly clusterable. Various max-stable process models were then fitted to each cluster of each variable, and the Schlather model with several covariance functions was found to be a good fit on both datasets compared to the Smith model with the Gaussian covariance function. The modelling approach presented in this paper could be useful to hydrologists, meteorologists and climatologists, including decision-makers in the agricultural sector, in enhancing their understanding of the behaviour of drought caused by extremely high temperatures and low rainfall. The modelling of these compound extremes could also assist in assessing the impact of climate change. It can be seen from this study that the size, including the topography of the location (cluster/region), provides important information about the strength of the extremal dependence.