## 4 Conclusions and Future Work  
Accurate forecasting of streamflow is a fundamental issue of interest to water resources engineers, scientists, and radiologists. This research work implements and evaluates the efficiency of standalone (OPELM and CHAID) models for two different rivers, including Baranduzchai and Nazluchai in ULB, Iran. To access the optimum input variables, the PACF, which considered identifying the statistically significant lagged data to construct the models, was applied to select the relevant input variables of the final model for predicting streamflow. The inputs and the output quantities of the models were split into two subsets including calibration (70% of total dataset) and validation (30% of total dataset) phases, and then whole dataset was normalized as the pre-processing data phase in order to change the values of numeric columns in the dataset to a common scale. The performance of the developed models was evaluated in terms of R, RMSE, NSE, MAE, and RSD.  
Afterward, to improve model performance for prediction of streamflow, the stochastic term of streamflow models was calculated by the ARCH model that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms. Therefore, the suitability of two hybrid models, ARCH-OPELM and ARCH-CHAID, has been examined and compared against standalone models (OPELM and CHAID) for streamflow modeling at two candidate study stations in ULB. The results remarkably reveal that ARCH-CHAID models in both stations outperformed all other models. Besides, standalone CHAID models have better results than OPELM methods. While ARCH-OPELM and OPELM models have ranked third and fourth in predicting monthly streamflow. As a conclusion, it is worth mentioning that the new hybrid \"ARCH-DDM\" models outperformed standalone models in predicting streamflow.  
For future research, it could be recommended that the use of data pre-processing techniques like empirical mode decomposition (EMD), ensemble EMD, and other new hybrid models like GARCH-CHAID (OPELM), MGARCH-CHAID (OPELM), and coupling approaches in the application of other hydrological parameters like rainfall, runoff, etc. can be addressed.  
N.F.A. prepared the conceptualization of the manuscript together with M.R.-B. and preformed methodology. Format analysis is carried out by N.F.A., S.F.N., M.R.-B., and D.N.K. [PERSON] with the help of N.F.A. wrote the original draft. Visualization applied by Q.B.P., T.D.D., and A.N.A. Data-driven methods are implemented by S.F.N. and M.R.-B. Also, A.N.A., S.P., T.D.D., P.T.T.N., and A.E.-S. wrote, reviewed, and edited the manuscript. Project administration is processed by C.M.F. [PERSON], M.R.-B., and [PERSON]-S. were the supervised authors. All authors have read and agree to the published version of the manuscript.  
This research received no external funding.  
The authors would like to appreciate the financial support received from Bold 2025 grant coded RJO: 10436494 by Innovation & Research Management Center (iRMC), Universiti Tenaga Nacional (UNITEN),Malaysia. The authors gratefully thank the Islamic Republic of Iran Meteorological Organization (IRIMO) for access to the weather station data.  
The authors declare no conflict of interest.