Mathematical Modelling and Applications

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Fitting Time-series Models to Kisumu Rainfall Data for the Period 1961-2014

Received: Jan. 16, 2020    Accepted: Feb. 06, 2020    Published: Feb. 19, 2020
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Abstract

Many small-scale farmers require adequate forecasts to help them plan for the rainfall. The National Meteorological Service provides forecasts seasonally, monthly and weekly. The forecasts are qualitative in nature hence inform, but cannot be directly used with decision support models. It is therefore important to consider forecast methods that researchers can use to generate quantitative data that can be applied in the models. In particular, an increasing need for forecasting daily rainfall data. In this study, the ARIMA and VAR models have been used to forecast five time period data for daily, monthly and seasonal rainfall data. The objective was to find the model parameters that best fit the three time periods. Fifty-year data from Kenya Meteorological Station, Kisumu, was used for the analysis. For each time period, five events were used as the test dataset. The ARIMA model was found to be best for forecasting daily rainfall in comparison to the VAR model, while SARIMA was best for monthly and seasonal data. One difference was done for the seasonal rainfall total, but not for monthly and monthly rainfall data. The VAR models included the available daily minimum and maximum temperatures. However, forecasted daily rainfall deviated from the test data, while monthly and seasonal data deviated even more.

DOI 10.11648/j.mma.20200501.14
Published in Mathematical Modelling and Applications ( Volume 5, Issue 1, March 2020 )
Page(s) 39-46
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, Sarima, VAR, Rainfall Data

References
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[2] Somvanshi, V. K., Pandey, O. P., Agrawal, P. K., Kalanker, N. V., Prakash, M. R. and Chand, R., 2006. Modeling and prediction of rainfall using artificial neural network and ARIMA techniques. J. Ind. Geophys. Union, 10 (2), pp. 141-151.
[3] Rose, D. C., Sutherland, W. J., Parker, C., Lobley, M., Winter, M., Morris, C., Twining, S., Ffoulkes, C., Amano, T. and Dicks, L. V., 2016. Decision support tools for agriculture: Towards effective design and delivery. Agricultural systems, 149, pp. 165-174.
[4] Cologni, A. and Manera, M., 2008. Oil prices, inflation and interest rates in a structural cointegrated VAR model for the G-7 countries. Energy economics, 30 (3), pp. 856-888.
[5] Psilovikos, A. and Elhag, M., 2013. Forecasting of remotely sensed daily evapotranspiration data over Nile Delta region, Egypt. Water resources management, 27 (12), pp. 4115-4130.
[6] Cropwat, F. A. O., 1992. A computer program for irrigation Planning and Management, By M. Smith. FAO Irrigation and Drainage Paper, (46).]
[7] Weesakul, U. and Lowanichchai, S., 2005. Rainfall forecast for agricultural water allocation planning in Thailand. Science & Technology Asia, pp. 18-27.
[8] Dungey, M. and Pagan, A., 2000. A structural VAR model of the Australian economy. Economic record, 76 (235), pp. 321-342.
[9] Landeras, G., Ortiz-Barredo, A. and López, J. J., 2009. Forecasting weekly evapotranspiration with ARIMA and artificial neural network models. Journal of irrigation and drainage engineering, 135 (3), pp. 323-334.
[10] Shilenje, Z. W. and Ogwang, B. A., 2015. The role of Kenya meteorological service in weather early warning in Kenya. International Journal of Atmospheric Sciences, 2015.
[11] Nugroho, A., Hartati, S. and Mustofa, K., 2014. Vector Autoregression (Var) Model for Rainfall Forecast and Isohyet Mapping in Semarang–Central Java–Indonesia. Editorial Preface, 5 (11).
[12] Adamowski, J. F., 2008. Peak daily water demand forecast modeling using artificial neural networks. Journal of Water Resources Planning and Management, 134 (2), pp. 119-128.
[13] Abdul-Aziz, A. R., Anokye, M., Kwame, A., Munyakazi, L. and Nsowah-Nuamah, N. N. N., 2013. Modeling and forecasting rainfall pattern in Ghana as a seasonal ARIMA process: The case of Ashanti region. International Journal of Humanities and Social Science, 3 (3), pp. 224-233.
[14] Jones, J. W., Hoogenboom, G., Porter, C. H., Boote, K. J., Batchelor, W. D., Hunt, L. A., Wilkens, P. W., Singh, U., Gijsman, A. J. and Ritchie, J. T., 2003. The DSSAT cropping system model. European journal of agronomy, 18 (3-4), pp. 235-265.
[15] Jones, S. S., Evans, R. S., Allen, T. L., Thomas, A., Haug, P. J., Welch, S. J. and Snow, G. L., 2009. A multivariate time series approach to modeling and forecasting demand in the emergency department. Journal of biomedical informatics, 42 (1), pp. 123-139.
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  • APA Style

    Mawora Thomas Mwakudisa, Edgar Ouko Otumba, Joyce Akinyi Otieno. (2020). Fitting Time-series Models to Kisumu Rainfall Data for the Period 1961-2014. Mathematical Modelling and Applications, 5(1), 39-46. https://doi.org/10.11648/j.mma.20200501.14

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    ACS Style

    Mawora Thomas Mwakudisa; Edgar Ouko Otumba; Joyce Akinyi Otieno. Fitting Time-series Models to Kisumu Rainfall Data for the Period 1961-2014. Math. Model. Appl. 2020, 5(1), 39-46. doi: 10.11648/j.mma.20200501.14

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    AMA Style

    Mawora Thomas Mwakudisa, Edgar Ouko Otumba, Joyce Akinyi Otieno. Fitting Time-series Models to Kisumu Rainfall Data for the Period 1961-2014. Math Model Appl. 2020;5(1):39-46. doi: 10.11648/j.mma.20200501.14

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  • @article{10.11648/j.mma.20200501.14,
      author = {Mawora Thomas Mwakudisa and Edgar Ouko Otumba and Joyce Akinyi Otieno},
      title = {Fitting Time-series Models to Kisumu Rainfall Data for the Period 1961-2014},
      journal = {Mathematical Modelling and Applications},
      volume = {5},
      number = {1},
      pages = {39-46},
      doi = {10.11648/j.mma.20200501.14},
      url = {https://doi.org/10.11648/j.mma.20200501.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.mma.20200501.14},
      abstract = {Many small-scale farmers require adequate forecasts to help them plan for the rainfall. The National Meteorological Service provides forecasts seasonally, monthly and weekly. The forecasts are qualitative in nature hence inform, but cannot be directly used with decision support models. It is therefore important to consider forecast methods that researchers can use to generate quantitative data that can be applied in the models. In particular, an increasing need for forecasting daily rainfall data. In this study, the ARIMA and VAR models have been used to forecast five time period data for daily, monthly and seasonal rainfall data. The objective was to find the model parameters that best fit the three time periods. Fifty-year data from Kenya Meteorological Station, Kisumu, was used for the analysis. For each time period, five events were used as the test dataset. The ARIMA model was found to be best for forecasting daily rainfall in comparison to the VAR model, while SARIMA was best for monthly and seasonal data. One difference was done for the seasonal rainfall total, but not for monthly and monthly rainfall data. The VAR models included the available daily minimum and maximum temperatures. However, forecasted daily rainfall deviated from the test data, while monthly and seasonal data deviated even more.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Fitting Time-series Models to Kisumu Rainfall Data for the Period 1961-2014
    AU  - Mawora Thomas Mwakudisa
    AU  - Edgar Ouko Otumba
    AU  - Joyce Akinyi Otieno
    Y1  - 2020/02/19
    PY  - 2020
    N1  - https://doi.org/10.11648/j.mma.20200501.14
    DO  - 10.11648/j.mma.20200501.14
    T2  - Mathematical Modelling and Applications
    JF  - Mathematical Modelling and Applications
    JO  - Mathematical Modelling and Applications
    SP  - 39
    EP  - 46
    PB  - Science Publishing Group
    SN  - 2575-1794
    UR  - https://doi.org/10.11648/j.mma.20200501.14
    AB  - Many small-scale farmers require adequate forecasts to help them plan for the rainfall. The National Meteorological Service provides forecasts seasonally, monthly and weekly. The forecasts are qualitative in nature hence inform, but cannot be directly used with decision support models. It is therefore important to consider forecast methods that researchers can use to generate quantitative data that can be applied in the models. In particular, an increasing need for forecasting daily rainfall data. In this study, the ARIMA and VAR models have been used to forecast five time period data for daily, monthly and seasonal rainfall data. The objective was to find the model parameters that best fit the three time periods. Fifty-year data from Kenya Meteorological Station, Kisumu, was used for the analysis. For each time period, five events were used as the test dataset. The ARIMA model was found to be best for forecasting daily rainfall in comparison to the VAR model, while SARIMA was best for monthly and seasonal data. One difference was done for the seasonal rainfall total, but not for monthly and monthly rainfall data. The VAR models included the available daily minimum and maximum temperatures. However, forecasted daily rainfall deviated from the test data, while monthly and seasonal data deviated even more.
    VL  - 5
    IS  - 1
    ER  - 

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Author Information
  • Department of Statistics and Actuarial Science, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya

  • Department of Statistics and Actuarial Science, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya

  • Department of Statistics and Actuarial Science, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya

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