This paper develops a method for nonlinear regression models estimation that is robust to heteroscedasticity and autocorrelation of errors. Using nonlinear least squares estimation, four popular growth models (Exponential, Gompertz, Verhulst, and Weibull) were computed. Some assumptions on the errors of these models (independence, normality, and homoscedasticity) being violated, the estimates are improved by modeling the residuals using the ETS method. For an application purpose, this approach has been used to predict the daily cumulative number of novel coronavirus (COVID-19) cases in Africa for the study period, from March 13, 2020, to June 26, 2021. The comparison of the proposed model to the competitors was done using statistical metrics such as MAPE, MAE, RMSE, AIC, BIC, and AICc. The findings revealed that the modified Gompertz model is the most accurate in forecasting the total number of COVID-19 cases in Africa. Moreover, the developed approach will be useful for researchers and policymakers for predicting purpose and for better decision making in different fields of its applications.
