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This work provides a general overview and consideration of Box-Jenkins models for temporal data and its extension known as Fourier residual autoregressive moving average models. We examined the modeling and forecasting of malaria incidence rate during pregnancy at Bishop Shannahan Hospital, Nsukka using Autoregressive Integrated Moving Average (ARIMA) Models propounded by Box and Jenkins. We adoptted the Box-Jenkins methodology to build ARIMA model for malaria incidences during pregnancy for a period of 10 years spanning from January 2006 to December 2016. Among the candidate models considered, ARIMA (3,1,1) was identified to be the most robust based on some model performance measures. The model was further improved upon by incorporating Fourier residual modification on the fitted ARIMA model. The Fourier Residual Autoregressive Moving Average (FARIMA) model obtained yielded improved result. Besides, model evaluation criterion such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Bias Error (MBE), Mean Bias Error (MBE), Mean Absolute Scaled Error (MASE), were used to access the models. FARIMA Model out performed ARIMA Model. Several time series plots and tests like augmented dickey fuller test, correlogram, Ljung-Box test for serial correlation of the residuals, etc were carried out in this study to test for stationarity, identify the order of ARIMA model and serial correlation residual respectively.

On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women