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

Chinonso Micheal Eze; Oluchukwu Chukwuemeka Asogwa; Charity Uchenna Onwuamaeze; Nnaemeka Martin Eze; Chukwunenye Ifeanyi Okonkwo

doi:doi:10.11648/j.ajtas.20200901.11

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

Chinonso Micheal Eze, Oluchukwu Chukwuemeka Asogwa, Charity Uchenna Onwuamaeze, Nnaemeka Martin Eze, Chukwunenye Ifeanyi Okonkwo

Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 1)

Received: 10 February 2020 Accepted: 3 April 2020 Published: 13 April 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 9, Issue 1)
DOI	10.11648/j.ajtas.20200901.11
Page(s)	1-7
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

ARIMA, Modeling, Forecasting, FARIMA, Model Performance Measures

References

[1]	Aniefiok, I. I and Murphy, D. (2017). Mixed seasonal and subset fourier model with seasonal Harmonics. Science Journal of applied mathematics and statistics. Vol. 5 (1): 1-9.
[2]	Box, G. E., and Jenkins, G. M. (1976). Time Series Analysis: Forcasting and Control. San Francisco: Holden-Day.
[3]	Brabin, B. J. (1983). An analysis of malaria in pregnancy in Africa. Bulletin of the World Health Organization, 61 (6): 1005-1016.
[4]	Ekezie, d. Opara, j., and Okenwe, I (2014). Modeling and Forecasting Malaria Mortality Rate using SARIMA Models (A Case Study of Aboh Mbaise General Hospital, Imo State Nigeria). Science Journal of Applied Mathematics and Statistics 2014; 2 (1): 31-41.
[5]	Federal Ministry of Health. Malaria situation analysis document. Nigeria: Federal Ministry of Health; 2001. p. 14.
[6]	McMichael, A. J., Woodruff, R. E and Hales, S. (2006). Climate change and human health: present and future risks. Lancet 2006, 367: 859-869.
[7]	Nguyen, T., Chen, P and Huang, Y. (2013). Forecasting with fourier residual modified ARIMA model – An emperical case of inbound tourism demand in New Zealand. Recent researches in applied economics and management. Vol. 2.
[8]	Prajakta, S. K. (2004). Time Series Forecasting Using Holt-Winters Exponential Smoothing. Kanwal Rekhi School of Information Technology, 4329008, 1-13.
[9]	Sachs, J and Malaney, P. (2002). The Economic and Social Burden of Malaria. Macmillan Publisher. Ltd.
[10]	Shu, M., Hsu, B and Nguyen, T. (2013). Forecasting international tourism deman – An emperical case of Thaiwan. Asian journal of emperical research. Vol. 3 (6), 711-724.
[11]	Thomson C. M, Mason J. S, Phindelia, T and Connor J. S. (2005). Use of Rainfall and Sea Surface Temperature Monitoring for Malaria Early Warning in Botswana. American Journal Tropical Medicine and Hygiene 73 (1), pp. 214-221.
[12]	Wangdi, K., Pratap, S. Tassanee, S., Saranath, L., Nicholas, J and Jaranit, K. (2010). Development of temporal modeling for forecasting and prediction of malaria infections using time-series and ARIMAX analyses: A case study in endemic district of Bhutai. Journal of Malaria. Vol. 9, pg. 251.

Cite This Article

Plain Text BibTeX RIS

APA Style

Chinonso Micheal Eze, Oluchukwu Chukwuemeka Asogwa, Charity Uchenna Onwuamaeze, Nnaemeka Martin Eze, Chukwunenye Ifeanyi Okonkwo. (2020). On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women. American Journal of Theoretical and Applied Statistics, 9(1), 1-7. https://doi.org/10.11648/j.ajtas.20200901.11

Copy | Download

ACS Style

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. Am. J. Theor. Appl. Stat. 2020, 9(1), 1-7. doi: 10.11648/j.ajtas.20200901.11

Copy | Download

AMA Style

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. Am J Theor Appl Stat. 2020;9(1):1-7. doi: 10.11648/j.ajtas.20200901.11

Copy | Download

@article{10.11648/j.ajtas.20200901.11,
  author = {Chinonso Micheal Eze and Oluchukwu Chukwuemeka Asogwa and Charity Uchenna Onwuamaeze and Nnaemeka Martin Eze and Chukwunenye Ifeanyi Okonkwo},
  title = {On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ajtas.20200901.11},
  url = {https://doi.org/10.11648/j.ajtas.20200901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200901.11},
  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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women
AU  - Chinonso Micheal Eze
AU  - Oluchukwu Chukwuemeka Asogwa
AU  - Charity Uchenna Onwuamaeze
AU  - Nnaemeka Martin Eze
AU  - Chukwunenye Ifeanyi Okonkwo
Y1  - 2020/04/13
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200901.11
DO  - 10.11648/j.ajtas.20200901.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200901.11
AB  - 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.
VL  - 9
IS  - 1
ER  -

Copy | Download

Author Information

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Chinonso Micheal Eze, Oluchukwu Chukwuemeka Asogwa, Charity Uchenna Onwuamaeze, Nnaemeka Martin Eze, Chukwunenye Ifeanyi Okonkwo. (2020). On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women. American Journal of Theoretical and Applied Statistics, 9(1), 1-7. https://doi.org/10.11648/j.ajtas.20200901.11

Copy | Download

ACS Style

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. Am. J. Theor. Appl. Stat. 2020, 9(1), 1-7. doi: 10.11648/j.ajtas.20200901.11

Copy | Download

AMA Style

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. Am J Theor Appl Stat. 2020;9(1):1-7. doi: 10.11648/j.ajtas.20200901.11

Copy | Download

@article{10.11648/j.ajtas.20200901.11,
  author = {Chinonso Micheal Eze and Oluchukwu Chukwuemeka Asogwa and Charity Uchenna Onwuamaeze and Nnaemeka Martin Eze and Chukwunenye Ifeanyi Okonkwo},
  title = {On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ajtas.20200901.11},
  url = {https://doi.org/10.11648/j.ajtas.20200901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200901.11},
  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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women
AU  - Chinonso Micheal Eze
AU  - Oluchukwu Chukwuemeka Asogwa
AU  - Charity Uchenna Onwuamaeze
AU  - Nnaemeka Martin Eze
AU  - Chukwunenye Ifeanyi Okonkwo
Y1  - 2020/04/13
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200901.11
DO  - 10.11648/j.ajtas.20200901.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200901.11
AB  - 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.
VL  - 9
IS  - 1
ER  -

Copy | Download