Development of a time series model to forecast rainfall data in Mwanza region,Tanzania

Climatic variations more or less decide the environment dynamics of an area. Extreme rainfall causes problems in any area, especially to the agriculturally sector. This study explored matters associated with modeling, identification techniques, diagnostic and forecasting of the time series of rainfall data in the Mwanza region using Box-Jenkins methodology. The procedure used in evaluating models and forecasting was through the use of monthly data from 1960 to 2000. The rainfall time series are not characterized by trends, such that, forms of transformations were not necessary, such as differencing and natural logarithm suggesting that the series is stationary. Only seasonal differencing was recommended as suggested by Box-Jenkins, implying that monthly rainfall time series are characterized by seasonality. Plotting of the original data was performed, and discussion for their practical problems has been done in order to achieve stationary of the series. In the identification, estimation and diagnostic checking stage, the study of the sample autocorrelations and partial autocorrelations was done in order to identify the model and estimate the associated parameters. Formal test statistics such as Akaike information Criterion were applied to verify the model that is adequate. Four possible seasonal time series models for monthly series were compared to find the adequate one. The adequate model was used to forecast the monthly rainfall data for the year 2001. The forecasts have been compared with the actual values and the empirical evaluation has been performed based on the percent prediction limit. Since the forecast values are reasonable, and are within the prediction limits, we conclude that the identified model can be taken for the respective series. Models can be used as general guide lines to understand probable future conditions that may occur.