Modeling residual components and irregular fluctuations in health time series

This study provides an in-depth analysis of methods for modeling residual components in time series applied to health data. Time series analysis plays a crucial role in many disciplines, particularly in public health. Time series make it possible to study the evolution of phenomena over time in order to identify trends and formulate forecasts. However, beyond the trend and seasonality components, residual components, often perceived as "noise", also contain valuable information that could impact the results of these forecasts if they are not taken into account. After exploring some methods (statistical and machine learning), we applied the first-order autoregressive method AR(1) to health data from the Cameroonian Ministry of Public Health for the period 2018 to 2022. This method successfully captured the relevant information contained in the residuals of our decomposition, achieving a performance of 99% in the test. This result is well beyond those using neural networks (LSTM) and ARIMA-ARCH on the same dataset. The study of the residuals helps to better adjust the general trend of the series and highlights the importance of taking into account the residuals in the modeling of time series in order to improve the accuracy of forecasts. Finally, this study opens up perspectives for the application of other hybrid modeling techniques combining statistical and machine learning methods for a more detailed analysis of health data.