Application of the Box-Jenkins, Time Series Models to the Monthly Rainfall in Gadaref State

Abstract

In this research the one of the Box-Jenkins time series models has been applied for the monthly rainfall average for the period (1970-2000), in the Gaderef State. From the estimated autocorrelation and partial autocorrelation coefficient it is noticeable that the time series of monthly rainfall is not stationary and it is containing the effect of seasonality component, and it is clear that the series repeated itself at each 12-month intervals. Therefore to make this series stationary, the first-order differences and eleventh order differences are taken, and to remove the seasonality spikes, the differences of degree (12) are taken. From the re-estimation of the autocorrelation and partial autocorrelation it is manifested that the appropriate model is the multiplicative seasonal model ARIMA (5, 1, 0) × (6, 11,1)12, and the suggested model is good and it gives precise forecasts according to Akaik's Information Criteria (AIC). Finally the monthly rainfall from June, 2000 to December 2001 are forecasted.