Estimation of Extreme Quantiles of Confirmed COVID-19 Cases Using South African Data

Forecasting is important in any scientific field, including COVID-19 epidemiology. Daily confirmed COVID-19 cases are in different phases characterised by peaks, making it difficult for most mathematical models to handle. In such cases, extreme value theory plays a critical role because values of interest are usually far away from the mean. In this paper, we develop mathematical models using Extreme values to capture uncertainties of forecasts associated with the COVID-19 pandemic using real-time data. A three-stage approach to probabilistic forecasting is used in this study. The stochastic gradient boosting, generalised additive model, additive quantile regression, and the nonlinear quantile regression are used to predict extremely high quantiles, i.e. 0.95-, 0.99- and 0.995-quantiles. The second stage combines each model's predicted extremely high quantiles using the weighted mean and median methods. The pinball loss and coverage probabilities are used to evaluate the accuracy of the predictions in the third stage. For all the extreme quantiles, i.e. the 0.95-, 0.99- and 0.995-quantiles, the cubic spline regression method gives the best predictions based on the lowest pinball losses, which are 171.41, 563.49 and 115.28, respectively. The weighted mean average model dominated by the mean is the second best based on the pinball losses but the best based on the coverage probability. This study provides insights into the strengths and weaknesses of different models for short-term extreme quantile prediction of COVID-19. Estimating extreme quantiles of daily COVID-19 using models with high predictive capabilities, such as the weighted mean-median model dominated by the mean, is important to public health officials and policymakers for planning and preparing for potential surges in CoVID-19 cases and similar pandemics in the future.