American Journal of Theoretical and Applied Statistics

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

Received: 10 February 2020    Accepted: 03 April 2020    Published: 13 April 2020
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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.

DOI 10.11648/j.ajtas.20200901.11
Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 1, January 2020)
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), 2024. 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.
Author Information
  • Department of Statistics, Faculty of Physical Science, University of Nigeria, Nsukka, Nigeria

  • Department of Maths, /Comp. Sc. /Stats. /Infor., Faculty of Science, Alex Ekwueme Federal University, Ndufu-Alike Ikwo, Ebonyi State, Nigeria

  • Department of Statistics, Faculty of Physical Science, University of Nigeria, Nsukka, Nigeria

  • Department of Statistics, Faculty of Physical Science, University of Nigeria, Nsukka, Nigeria

  • Department of Maths, /Comp. Sc. /Stats. /Infor., Faculty of Science, Alex Ekwueme Federal University, Ndufu-Alike Ikwo, Ebonyi State, Nigeria

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    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

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    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

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    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

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  • @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://download.sciencepg.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}
    }
    

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