Modelling and Forecasting of Rainfall Time Series Using SARIMA

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly, weekly and daily monsoon rainfall time series. Using Box-Cox transformation and subsequently differencing, monthly, weekly and daily monsoon rainfall time series were made stationary. The best SARIMA models were selected based on the autocorrelation function (ACF) and partial autocorrelation function (PACF), and the minimum values of Akaike Information Criterion (AIC) and Schwarz Bayseian Information (SBC). As per Ljung-Box Q statistics, residuals were random in nature and there was no need for further modelling. Performance and validation of the SARIMA models were evaluated based on various statistical measures. The mean and standard deviation of the predicted data were found close to the observed data. Nash-Sutcliffe coefficient also indicated a high degree of model fitness to the observed data. Forecasting of monthly, weekly, daily monsoon time series for 14 years, i.e., from 2014 to 2027 was done using the developed SARIMA models.