Monthly streamflow prediction using a hybrid stochastic-deterministic approach for parsimonious non-linear time series modeling

Zhen Wang, Nasrin Fathollahzadeh Attar, Keivan Khalili, Javad Behmanesh, Shahab S. Band, Amir Mosavi, Kwok wing Chau

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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.

Original languageEnglish
Pages (from-to)1351-1372
Number of pages22
JournalEngineering Applications of Computational Fluid Mechanics
Issue number1
Publication statusPublished - 1 Jan 2020


  • gene expression programming
  • Integrated hybrid models
  • nonlinear time series models
  • stochastic and deterministic
  • streamflow modeling
  • Urmia Lake basin

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation

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