A Copula-Enhanced ARMA-GARCH Framework for Rainfall Analysis
DOI:
https://doi.org/10.11113/mjfas.v22n4.5055Keywords:
ARMA; GARCH; Box-Jenkins; Copula; ForecastAbstract
Accurate rainfall simulation is essential for hydrological risk assessment and water resources management. The ARMA-GARCH models effectively capture temporal dependence and volatility in rainfall series and copula models are frequently used to represent the joint dependence among rainfall stations. However, it is generally assumed that modelling cross-station dependence will improve forecasting performance, with limited attention given to whether sufficient residual dependence remains after temporal filtering to justify the additional modelling complexity. Hence, this study investigates whether incorporating copula-based dependence modelling provides additional benefits for rainfall simulation after ARMA-GARCH filtering. Daily rainfall data from three meteorological stations were first modelled using ARMA-GARCH, and the standardized residuals were transformed to uniform margins. Residual dependence was then evaluated using Kendall's tau and empirical upper tail dependence before fitting multivariate copula models. The dependence analysis revealed weak residual association among the stations, with Kendall's tau values ranging from 0.01 to 0.05. Although weak upper tail dependence was observed at the 90th percentile threshold, it decreased to approximately zero at higher thresholds, indicating limited co-occurrence of extreme rainfall events after temporal filtering. The forecasting comparison showed that the ARMA-GARCH model achieved lower MAE, MSE and RMSE values than the ARMA-GARCH-copula framework. These findings suggest that, for the selected rainfall stations, modelling the remaining cross-station dependence after temporal filtering contributed only modestly to forecasting performance. This study highlights the importance of evaluating residual dependence before introducing copula-based dependence structures in multisite rainfall modelling
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