A STATISTICAL ANALYSIS OF RAINFALL IN SINGAPORE

Abstract

In Singapore, the prevalence of the North-East and SouthWest monsoons over the periods of November to March and May to September respectively, seem to indicate that cur monthly rainfall could possess a seasonality of about six months in period. However, whether such pattern is significant is not clear without furthur analysis. Hence, it is necessary to do a time series analysis on the data, in order to extract more accurate information about how the pattern of Singapore's monthly rainfall varies over time, for the important purpose of making forecasts. This exercise adopts one of the most effective and versatile method of analysing time series - the Box-Jenkins approach, to analyse our monthly rainfall data in millimeters, over a period of 15 years or 192 months, from January 1969 to December 1984. First, common models employed in the Box-Jenkins methodology are introduced with the important concepts of stationarity, autocorrelations and partial autocorrelations. Next, the process or model building which involves the Box-Jenkins three-stage cycle of identification, estimation and diagnostic checking for these models is discussed. Thereafter, it is shown how a satisfactory fitted model can be used for forecasting future time series values. After laying the theoretical groundwork of the Box-Jenkins approach to time series modelling, the final part of this exercise comprises of its application in fitting appropriate model(s) to our log-transformed rainfall data. Two models, the ARMA(1,1) and the AR(l) model, are considered, Between the two, the ARMA(1,1) was found to be the legitimate model in terms of having fulfilled requirements in diagnostic checking. Although inadequacy was detected in the AR(l) model, it is not completely discarded due to its more parsimonious nature and satisfactory forecasting performance.