## 1 Introduction
To overcome this issue, it would be worthwhile for experts to endeavor to use linear and non-linear time-series models (e.g., AR, ARMA, ARIMA, ARCH, Smooth Transition Autoregressive (STAR), Self-Exciting Threshold Autoregressive (SETAR), Bilinear models) to define the stochastic parts of models [23; 24; 25; 26; 27], which are widely used in predicting hydrological variables like precipitation [28; 29], streamflow [30; 31], and runoff [32; 33]. Several studies have carried out nonlinear, parametric and nonparametric methods like ARCH, STAR, SETAR [20; 34] in predicting streamflow from reservoirs [35; 36; 37; 38; 12], in modeling stage-discharge curves [39; 40], and in the impact of climate change on runoff [41]. The use of hybrid models in both AIs and time-series methods has been recently conducted by researchers worldwide [42; 43; 44; 45; 46; 47]. The main goal of utilizing hybrid methods is to make prediction models concise by producing very remarkable and reliable results. [PERSON] et al. developed a nonlinear hybrid time-series, namely SETAR-GARCH, generalized autoregressive conditional heteroscedasticity, modeling streamflow in the case of Zarrineh Rood River at Urmia Lake Basin (ULB). They found that SETAR-GARCH models performed better than the models without GARCH, showing that the hybrid method performed better in modeling than sole models [48]. However, the integration of AI and time-series methods with accuracy and optimum results is still scarce for hydrological phenomena such as streamflow. [PERSON] et al. proposed two new combined models of GEP-ARCH and ANN-ARCH methods in estimation of monthly rainfall in five selected stations of Iran. Their outcomes indicated that hybrid models outperform the sole models [49]. The core objective of the present research is to develop a stronger and more accurate model for predicting monthly streamflow data using its antecedent values at two stations of Tapik and Dizaj in the Nazluchai and Baranduzchai rivers located in ULB of Iran, respectively for a period of 31 years. That is, this study aims to define new ARCH-type family models that can be used to obtain the stochastic terms of the streamflow equations. Although several studies have been carried out using linear and nonlinear time-series methods for hydrological forecasting, there is not any published work, to the best knowledge of the authors, related to the application of ARCH model integrated with two DDMs such as OPELM and CHAID (classification based technique) in predicting monthly streamflow. Another objective of this study is to assess the robustness of the hybrid OPELM/CHAID-ARCH vs. standalone models viz diagnostic evaluation of performance with visual plots and statistical score metrics of predicted and observed streamflow for the independent validation data. The rest of the present research is organized as follows. Section 2, which is considered as the materials and methods, includes Section 2.1, study area and data analysis; Sections 2.2-2.6, describing the methodology of nonlinear models (ARCH) and two DDMs (e.g., CHAID and OPELM) and their integration; and Section 2.7, describing the statistical performance indicators applied for this study. Sections 3.1-3.6 discusses the forecasting results of the proposed models and comparative results. Section 3.7 is the discussion and, finally, Section 4 presents a summary, future work, and the conclusion of the outline results are given.