Estimating the Risk of SARS-CoV-2 Deaths Using a Markov Switching-Volatility Model Combined with Heavy-Tailed Distributions for South Africa

Résumé

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. South Africa faced the highest number of casualties. This study aimed to estimate the risk of fatalities due to Covid-19 infection for an African country hard hit by the pandemic. The value-at-risk (VaR) concept in financial time series analysis is used to estimate the risk of deaths.Methods: In this study, the daily number of deaths due to Covid-19 infection is used. 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. The heavy-tailed distributions employed are the Student-t distribution (StD), Skewed Student-t distribution (SStD), normal reciprocal inverse Gaussian distribution (NRIGD), and Pearson type IV distribution (PIVD). Risk estimates were estimated using the value-at-risk (VaR) procedure. The model performances were assessed using the Kupiec likelihood ratio test.Results: The results indicate that the MS(3)-GARCH(1,1)-NRIGD is the best model at 90%. At 95% the MS(3)-GARCH(1,1)-SStD and MS(3)-GARCH(1,1)-PIVD are the best models, and MS(3)-GARCH(1,1)-StD, MS(3)-GARCH(1,1)-NRIGD, MS(3)-GARCH(1,1)-PIVD are the best at 97.5%. The MS(3)-GARCH(1,1)-NRIGD is the best model at 99%. Overall MS(3)-GARCH(1,1)-NRIGD is the best model, it outperforms all the models at almost all the levels. VaR estimates indicated that with a probability of 0.95, the number of deaths that will occur on the 27th, 28th and 29th of August 2021 will be greater than 278, 211, and 134 respectively, the actual values are 361, 274 and 134.Conclusion: The MS(3)-GARCH(1,1) model combined with heavy-tailed distributions provides a robust model for estimating the risk of death due to Covid-19. The accuracy of the volatility model is essential in forecasting the volatility of future health-related deaths in which the predictability of volatility plays an integral role in health risk management.

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