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Modelling epidemiological count time series using Integer-valued GARCH models embedded with Fourier terms |
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PP: 995-1012 |
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doi:10.18576/jsap/150403
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Author(s) |
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Thembhani Hlayisani Chavalala,
Retius Chifurira,
Knowledge Chinhamu,
Jacob Majakwara,
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Abstract |
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| Frequently, epidemiological count data are characterised by complex features such as overdispersion, serial autocorrelation, heteroscedasticity, and seasonal patterns. Poisson and Negative Binomial (NB)-INGARCH models have been extensively utilised to study and forecast datasets of this nature. These modelling frameworks do not account for the seasonal patterns that are often exhibited by the epidemiological time series. The inability to capture seasonality in the count time series process could lead to biased forecasts, misinterpretation of the underlying trends, and inadequate model performance. This, in turn, undermines the efficient allocation of essential resources such as healthcare personnel and vaccination programs. To ensure sound healthcare planning and timely interventions, effective modelling of epidemiological data remains fundamental. This study incorporates the Fourier components in the NB-INGARCH model to address the seasonality often exhibited in epidemiological data. For comparative analysis, various INGARCH models were fitted to the daily number of COVID-19 death cases in South Africa, and as well as in its three largest Provinces. The NB-INGARCH framework consistently outperformed the Poisson-INGARCH models, with the inclusion of Fourier terms further enhancing its effectiveness. Specifically, the NB-INGARCH(2,1) model incorporating Fourier harmonics successfully captured overdispersion, short-term dependence, heteroscedasticity, and weekly seasonality. The findings highlight that uniform seasonal adjustments may be inadequate, underscoring the need for tailored, region-specific modifications. A one-size-fits-all modelling approach risks oversimplifying the complexity and variability inherent in epidemiological count time series. |
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