Modelling Rainfall Series in North Central Nigeria: A Comparative Study of Box-Jenkins and State Space Model Approaches

This study aims at examining the performances of Box-Jenkins (BJ) and State Space (SS) modelling approaches, evidence from rainfall series of the North Central part of Nigeria. The study utilized monthly rainfall series of five North Central states of the country covering the period January 1961 to July 2019. This study employed the following methodologies: The Augmented Dickey-Fuller test for the non-seasonal stationarity check; HEGY test for the seasonal stationarity check; the Seasonal Auto-Regressive Integrated Moving Average modelling strategy of Box-Jenkins; and the State Space Local Level modelling with Seasonality. Among the 20 candidate BJ models estimated for each of the five states rainfall series, the study returned SARIMA(4,0,4)(1,0,0)₁₂, SARIMA(3,0,3)(2,0,0)₁₂, SARIMA(2,0,3)(1,0,0)₁₂, SARIMA(2,0,4)(1,0,0)₁₂ and SARIMA(4,0,2)(2,0,0)₁₂ as the most parsimonious BJ models for Benue, Niger, Kogi, Kwara and Federal Capital Territory (FCT) states respectively. Also, using the SS approach the study fitted Local Level Models with stochastic seasonality for each of the state rainfall series and were labelled SSBER, SSNIR, SSKOR, SSKWR and SSFCR for Benue, Niger, Kogi, Kwara and FCT states respectively. The forecasting performances of the most parsimonious SARIMA models and State Space Local Level Model with stochastic seasonality were examined. From the forecasts evaluation results, the RMSE, MAE, Theil’s U criteria and average of the three loss functions indicate that the state space local level model with seasonality outperformed the BJ models (SARIMA). In conclusion, SS models returned as more robust models compared to any BJ models (SARIMAs). Thus, it is evident that SS model is a noble intervention capable of modelling different features characteristic in a series such as trend and seasonality. The study therefore recommends the adoption of state space modelling approach based on the ability of the approach to accommodate distinct features instead of differencing (i.e. eliminating trend and seasonality).