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Volume 9, Issue 1, January 2020, Page: 1-7
On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women
Chinonso Micheal Eze, Department of Statistics, Faculty of Physical Science, University of Nigeria, Nsukka, Nigeria
Oluchukwu Chukwuemeka Asogwa, Department of Maths, /Comp. Sc. /Stats. /Infor., Faculty of Science, Alex Ekwueme Federal University, Ndufu-Alike Ikwo, Ebonyi State, Nigeria
Charity Uchenna Onwuamaeze, Department of Statistics, Faculty of Physical Science, University of Nigeria, Nsukka, Nigeria
Nnaemeka Martin Eze, Department of Statistics, Faculty of Physical Science, University of Nigeria, Nsukka, Nigeria
Chukwunenye Ifeanyi Okonkwo, Department of Maths, /Comp. Sc. /Stats. /Infor., Faculty of Science, Alex Ekwueme Federal University, Ndufu-Alike Ikwo, Ebonyi State, Nigeria
Received: Feb. 10, 2020;       Accepted: Apr. 3, 2020;       Published: Apr. 13, 2020
DOI: 10.11648/j.ajtas.20200901.11      View  318      Downloads  131
Abstract
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.
Keywords
ARIMA, Modeling, Forecasting, FARIMA, Model Performance Measures
To cite this article
Chinonso Micheal Eze, Oluchukwu Chukwuemeka Asogwa, Charity Uchenna Onwuamaeze, Nnaemeka Martin Eze, Chukwunenye Ifeanyi Okonkwo, On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women, American Journal of Theoretical and Applied Statistics. Vol. 9, No. 1, 2020, pp. 1-7. doi: 10.11648/j.ajtas.20200901.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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