Modelling Monthly Rainfall of Calabar, Nigeria Using Box-Jenkins (ARIMA) Method

Abstract

Rainfall has both positive and negative effects on human activities hence, correct prediction of the period of occurrence is very essential. However, the traditional method of predicting months of heavy rainfall is gradually fading out as irregular rainfall pattern is been experienced in most regions of the world. The rainfall pattern in Calabar city in Southern Nigeria has been reported in past literatures of being irregular. Hence, this research applied the Auto-Regressive Integrated Moving Average (ARIMA) also known as Box-Jenkins method to model the rainfall pattern of Calabar. This was achieved by subjecting 50years monthly rainfall (1971 – 2020) to gretl software version 2021b. The analysed data showed that the rainfall of the study area required just one-time differencing to attain stationarity at 95% confidence, while the order of the Auto-Regressive AR(p) and Moving Average MA(q) models were either 1 or 2 in both cases. Hence ARIMA(1,1,1), ARIMA(1,1,2), ARIMA(2,1,1) and ARIMA(2,1,2) were identified and further analyses revealed that ARIMA(2,1,2) best suited the rainfall of the study area. A diagnostic check was carried out on the selected ARIMA (2,1,2) model and it was observed to be reliable (minimal white noise) thereafter, it was used to forecast the rainfall of the study area for some months.

Keywords: Correlogram, Differencing, Stationarity, Time Series