Time series modelling and forecasting of the dynamics of infant mortalities in South Africa

Background Despite the significant progress made in child survival, there are still about 6500 daily newborn mortalities across the globe with sub-Saharan Africa, southern and central Asia bearing the heaviest burden. Prior studies frequently employed the Box-Jenkins framework to model and forecast infant mortality rates over time, although the daily infant deaths are count-based. The aim of this study was to evaluate and compare the performance of the traditional Box-Jenkins framework with a time series count-based process for modelling and forecasting the number of infant deaths in South Africa. Methods The Augmented Dickey-Fuller and Phillips-Perron tests revealed that the considered time series models should incorporate the trend and drift components. The ARIMA (2,0,1) with drift and trend components was fitted on the daily infant mortality data. Furthermore, the log-linear Poisson Autoregressive model that mimics the structure of an ARIMA (2,0,1) with drift and trend components was also considered for the same dataset. The residuals from both the fitted models were extracted and employed to assess how well the models fit the data. Key performance indicators were considered to determine which model provided the best fit for the data. Results Diagnostics tests confirmed that the two fitted models are adequate for the data. The Akaike Information Criterion and other model evaluation criteria’s demonstrate equivalent performance by the two models. For South Africa's data, both models revealed a negative trend coefficient, indicating a decline in infant mortality over time. Conclusion Model selection should be aligned with the characteristics of the data and analytical priorities. The log-linear Poisson autoregressive model is the most suitable framework for count-based time series like the daily number of infant deaths. The declining trend in infant mortality in South Africa suggests positive progress toward achieving Sustainable Development Goal 3.2, which targets ending preventable deaths of newborns and children under five.