Estimating the risk of SARS-CoV-2 deaths using a Markov switching-volatility model combined with heavy-tailed distributions for South Africa

Abstract

Abstract Background SARS-CoV-2 (Covid-19 virus) infection exposed the unpreparedness of African countries to health-related issues, South Africa included. Africa recorded more than 211 853 deaths as a consequence of Covid-19. When rare and deadly diseases require urgent hospitalisation strikes, governments and healthcare providers are usually caught unprepared, resulting in huge loss of lives. Usually, at the beginning of such pandemics, there is no rich data for health practitioners and academics to be able to forecast the number of patients or deaths related to the pandemic. This study aims to predict the number of deaths associated with Covid-19 infection. With the availability of the number of deaths on a daily basis, the results stemming from this study are important to inform and plan health policy. Methods This study uses the daily number of deaths due to Covid-19 infection. Exploratory data analysis reveals that the data exhibits non-normality, three structural breaks and volatility clustering characteristics. The Markov switching (MS)-generalized autoregressive conditional heteroscedasticity (GARCH)-type model combined with heavy-tailed distributions is fitted to the returns of the data. Using available daily reported Covid-19-related deaths up until 26 August 2021, we report 10-day ahead forecasts of deaths. All forecasts are compared to the actual observed values in the forecasting period. Results The Anderson–Darling Goodness of fit test confirms that the fitted models are adequate for the data. The Kupiec likelihood ratio test and the root mean square error (RMSE) were used to select the robust model at different risk levels. At 95% the MS(3)-GARCH(1,1) combined with Pearson’s type IV distribution (PIVD) is the best model. This indicates that the proposed best-fitting model is reasonable and can be used for predicting the daily number of deaths due to Covid-19. Conclusion The MS(3)-GARCH(1,1)-PIVD model provides a reliable and accurate method for predicting the minimum number of death due to Covid-19. The accuracy of the proposed model will assist policymakers, academics and health practitioners in forecasting the volatility of future health-related deaths in which the predictability of volatility plays an integral role in health risk management.

Keywords

• SARS-CoV-2 (Covid-19) infection
• Death
• Volatility models
• Value-at-risk
• Heavy-tailed distributions
• Structural breaks