# Optimal Stochastic Forecast Models of Rainfall in South-West Region of Nigeria

• J. N Onyeka-Ubaka Department of Mathematics, University of Lagos, Nigeria.
• M, A Halid Department of Mathematics, University of Lagos, Nigeria.
• R. K. Ogundeji Department of Mathematics, University of Lagos, Nigeria.
Keywords: Optimum Forecast, RFIMA, SARIMA, Model Diagnostics, Residuals

### Abstract

Rainfall estimates are important components of water resources applications, especially in agriculture, transport. constructing irrigation and drainage systems. This paper aims to stochastically model and forecast the rainfall trend and pattern for a city, each purposively selected in five states of the South-Western Region of Nigeria. The data collected from Nigerian Meteorological Agency (NIMET) website are captured with fractional autoregressive integrated moving average (ARFIMA) and seasonal autoregressive integrated moving average (SARIMA) models. The autocorrelation function (ACF) and partial autocorrelation function (PACF) are used for model identification, the models selected are subjected to diagnostic checks for the models adequacy. Several tests: Augmented Dickey Fuller (ADF), Ljung Box and Jarque Bera tests are used for investigating unit root, serial autocorrelation and normality of residuals, respectively; the mean square error, root mean square error and mean absolute error are employed in validating the optimal stochastic model for each city in all states, in which the model with the lowest error of forecasting of all competing models is suggested as the best. The analyses and findings suggest SARIMA(1,0,1)(1,1,0) [12], SARIMA(3,0,2)(1,0,0) [12], SARIMA(1,0,0)(1,1,0) [12], SARIMA(2,0,2)(2,1,0) [12] and SARIMA(0,0,1)(1,1,0) [12] for (Ibadan) Oyo State, (Ikorodu) Lagos State, (Osogbo) Osun State, (Abeokuta) Ogun State and (Akure) Ondo state, respectively. The seasonal ARIMA (SARIMA) model was proven to be the best optimal stochastic forecast model for forecasting rainfall in the selected cities. The SARIMA model was, therefore, recommended as a veritable technique that will assist decision makers (Government, Farmers, and Policymakers) to establish better strategies “aprior” on the management of rainfall against upcoming weather changes to ensure increase in agricultural yields for the betterment of the citizenry and general economic growth.

Published
2021-11-10
How to Cite
Onyeka-Ubaka, J. N., Halid, M. A., & Ogundeji, R. K. (2021). Optimal Stochastic Forecast Models of Rainfall in South-West Region of Nigeria. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 7(2), 1 - 20. https://doi.org/10.52968/28306097
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Articles