Improving Prediction Accuracy of Rainfall Time Series By Hybrid SARIMA–GARCH Modeling

In this paper, a hybrid of seasonal autoregressive integrated moving average (SARIMA)-generalized autoregressive conditional heteroscedasticity (GARCH) was applied to eliminate conditional variance of the SARIMA model of rainfall time series in two different climatic environments (Agartala: humid, and Jodhpur: arid). In addition, the effectiveness of data normalization techniques (differencing and transformation) to stabilize conditional variance in the SARIMA residuals is additionally examined. The residuals from SARIMA models were tested for heteroscedasticity, utilizing the McLeod–Li test, and demonstrated some autocorrelation. Then, the rainfall time series was transformed (differencing and Box–Cox) so that the effect of heteroscedasticity is eliminated. The hybrid SARIMA–GARCH model based on transformed rainfall time series resulted in good statistics performance indices at both climatic environments. The findings of the study suggest that the performance of SARIMA models can be enhanced by using appropriate transformation (Box–Cox) along with GARCH model of residuals of highly skewed rainfall time series from both climatic environments. For Agartala station of monthly rainfall time series, the best model was SARIMA (0, 1, 1) (0, 1, 1) 12 –GARCH (1, 2) with coefficient of determination ( R 2 ) = 0.72 and root-mean-square error (RMSE) = 25.22, but after Box–Cox transformation of data, the best model was SARIMA (0, 1, 1) (0, 1, 1) 12 –GARCH (2, 4) with R 2 = 0.87 and RMSE = 0.672. For the monthly rainfall series of Jodhpur station, the best model was SARIMA (0, 1, 1) (0, 1, 1) 12 –GARCH (1, 2) with R 2 = 0.68 and RMSE = 16.75, but after Box–Cox transformation of data the best model was SARIMA (0, 1, 1) (0, 1, 1) 12 –GARCH (1, 2) with R 2 = 0.79 and RMSE = 1.917. The performance indices indicate that hybrid (SARIMA–GARCH) models fitted to transformed time-series rainfall data performed best in the humid as well as the arid regions.