Time Series Analysis of Monthly Rainfall data for the Gadaref rainfall station, Sudan, by Sarima Methods

The time series being rainfall data is a typical seasonal series of one-year period. The time-plot of the realization herein called GASR and its correlogram are as expected, reflecting seasonality of period 12. For instance, the autocorrelation function is oscillatory of period 12. A 12-point differencing yields a series called SDGASR with a generally horizontal secular trend. It is adjudged stationary by the Augmented Dickey Fuller unit root test. Its correlogram gives an indication of stationarity as well as an involvement of the presence of a seasonal moving average component of order one and a seasonal autoregressive component of order two. This autocorrelation structure suggests three multiplicative SARIMA models, namely: (0, 0, 0)x(0, 1, 1)12 , (0, 0, 1)x(0, 1, 1)12 and (0, 0, 1)x(2, 1, 1)12. The first model is adjudged the most adequate. Its residuals have been observed to be uncorrelated. It may be the basis for the forecasting of rain in the region for planning purposes.