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.
Highlights
Rainfall estimates are important components of water resources applications
Several authors have written on seasonal autoregressive integrated moving average (SARIMA) models adopting several methods such as the non-parametric methods (Artificial Neural Networks) and Parametric Methods (Exponential smoothing, Extrapolation of trend curves, the Holt-Winters forecasting procedure and Box Jenkins procedure)
[3] Tariq and Abbasabd (2016) used a SARIMA model for Nyala station (Sudan), which was considered appropriate for forecasting monthly rainfalls
Summary
In the South-South region of Nigeria, [7] Etuk, et al (2013) fitted a long-range SARIMA(5, 1, 0)(0, 1, 1) model to rainfall data in Port Harcourt and observed that the fitted model was not fair because of the order of the non-seasonal autoregressive part. [9] Yaya, et al (2015) fitted trend and seasonal models to a rainfall data from different meteorological stations in the six geographical zones in Nigeria. The motivation and objective of this paper is to select the optimal stochastic model(s) from the different seasonal autoregressive integrated moving average (SARIMA) models and fractional autoregressive integrated moving average (AFRIMA) models, for forecasting rainfall in the South West Region of Nigeria.
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