Accurate streamflow prediction is essential in reservoir management, flood control, and operation of irrigation networks. In this study, the deterministic and stochastic components of modeling are considered simultaneously. Two nonlinear time series models are developed based on autoregressive conditional heteroscedasticity and self-exciting threshold autoregressive methods integrated with the gene expression programming. The data of four stations from four different rivers from 1971 to 2010 are investigated. For examining the reliability and accuracy of the proposed hybrid models, three evaluation criteria, namely the R², RMSE, and MAE, and several visual plots were used. Performance comparison of the hybrid models revealed that the accuracy of the SETAR-type models in terms of R² performed better than the ARCH-type models for Daryan (0.99), Germezigol (0.99), Ligvan (0.97), and Saeedabad (0.98) at the validation stage. Overall, prediction results showed that a combination of the SETAR with the GEP model performs better than ARCH-based GEP models for the prediction of the monthly streamflow.

Abbreviations: ADF = Augmented Dickey-Fuller; AIC = Akaike Information Criterion; ANFIS = Adaptive Neuro-Fuzzy Inference System; ANNs = Artificial Neural Networks; AR = Autoregressive Models; ARIMA = Autoregressive Integrated Moving Average; ARCH = Autoregressive Conditional Heteroscedasticity; ATAR = Aggregation Operator Based TAR; BL = Bilinear Models; BNN = Bayesian Neural Network; CEEMD = Complete Ensemble Empirical Mode Decomposition; DDM =Data-Driven Model; GA = Genetic Algorithm; GARCH = Generalized Autoregressive Conditional Heteroscedasticity; GEP = Gene Expression Programming; KNN = K-Nearest Neighbors; KPSS = Kwiatkowski–Phillips–Schmidt–Shin; LMR = Linear and Multilinear Regressions; LR = Likelihood Ratio; LSTAR = Logistic STAR; MAE = Mean Absolute Error; PACF = Partial Autocorrelation Function; PARCH = Partial Autoregressive Conditional Heteroscedasticity; R ² = Coefficient of Determination; RMSE = Root Mean Square Error; RNNs = Recurrent Neural Networks; SETARMA = Self-Exciting Threshold Autoregressive Moving Average; SETAR = Self-Exciting Threshold Autoregressive; STAR = Smooth Transition AR; SVR = Support Vector Regression; TAR = Threshold Autoregressive; TARMA = Threshold Autoregressive Moving Average; ULB = Urmia Lake Basin; VMD = Variational Mode Decomposition; WT = Wavelet Transforms

准确的流量预测对于水库管理，防洪和灌溉网络的运营至关重要。在这项研究中，同时考虑了建模的确定性和随机性。基于自回归条件异方差和自激阈值自回归方法，并结合基因表达程序，开发了两个非线性时间序列模型。研究了1971年至2010年来自四个不同河流的四个站点的数据。为了检查所提出的混合模型的可靠性和准确性，使用了三个评估标准，即R ²，RMSE和MAE，以及几个视觉图。混合模型的性能比较显示，SETAR型模型在R ²方面的准确性在验证阶段，Daryan（0.99），Germezigol（0.99），Ligvan（0.97）和Saeedabad（0.98）的性能优于ARCH型模型。总体而言，预测结果表明，SETAR与GEP模型的组合比基于ARCH的GEP模型对每月流量的预测效果更好。

缩略语：ADF =增强Dickey-Fuller；AIC =赤池信息准则；ANFIS =自适应神经模糊推理系统；ANNs =人工神经网络；AR =自回归模型；ARIMA =自回归综合移动平均线；ARCH =自回归条件异方差；ATAR =基于聚合算子的TAR；BL =双线性模型；BNN =贝叶斯神经网络；CEEMD =完整的集合经验模式分解；DDM =数据驱动模型；GA =遗传算法；GARCH =广义自回归条件异方差；GEP =基因表达编程；KNN = K最近邻居；KPSS = Kwiatkowski–Phillips–Schmidt–Shin；LMR =线性和多线性回归；LR =似然比；LSTAR =物流之星；MAE =平均绝对误差；PACF =部分自相关函数；R ²  =测定系数；RMSE =均方根误差；RNN =递归神经网络；SETARMA =自激阈值自回归移动平均值；SETAR =自激阈值自回归；STAR =平滑过渡AR；SVR =支持向量回归；TAR =阈值自回归；TARMA =阈值自回归移动平均线；ULB =乌尔米亚湖流域；VMD =变分模式分解；WT =小波变换