Research papersA comparison of monthly precipitation point estimates at 6 locations in Iran using integration of soft computing methods and GARCH time series model

•Monthly precipitation was modeled in this study.•Soft computing methods including MARS, BN and GEP were integrated with GARCH time series model.•Three novel hybrid models namely MARS-GARCH, BN-GARCH and GEP-GARCH were proposed.•Overall, MARS-GARCH and BN-GARCH had better performance than GEP-GARCH.•Peak points of precipitation data were well modeled in the proposed hybrid models.

Precipitation plays an important role in determining the climate of a region. Precise estimation of precipitation is required to manage and plan water resources, as well as other related applications such as hydrology, climatology, meteorology and agriculture. Time series of hydrologic variables such as precipitation are composed of deterministic and stochastic parts. Despite this fact, the stochastic part of the precipitation data is not usually considered in modeling of precipitation process. As an innovation, the present study introduces three new hybrid models by integrating soft computing methods including multivariate adaptive regression splines (MARS), Bayesian networks (BN) and gene expression programming (GEP) with a time series model, namely generalized autoregressive conditional heteroscedasticity (GARCH) for modeling of the monthly precipitation. For this purpose, the deterministic (obtained by soft computing methods) and stochastic (obtained by GARCH time series model) parts are combined with each other. To carry out this research, monthly precipitation data of Babolsar, Bandar Anzali, Gorgan, Ramsar, Tehran and Urmia stations with different climates in Iran were used during the period of 1965-2014. Root mean square error (RMSE), relative root mean square error (RRMSE), mean absolute error (MAE) and determination coefficient (R2) were employed to evaluate the performance of conventional/single MARS, BN and GEP, as well as the proposed MARS-GARCH, BN-GARCH and GEP-GARCH hybrid models. It was found that the proposed novel models are more precise than single MARS, BN and GEP models. Overall, MARS-GARCH and BN-GARCH models yielded better accuracy than GEP-GARCH. The results of the present study confirmed the suitability of proposed methodology for precise modeling of precipitation.