A Hybrid Model Integrating Elman Neural Network with Variational Mode Decomposition and Box–Cox Transformation for Monthly Runoff Time Series Prediction

Precise and reliable monthly runoff prediction plays a vital role in the optimal management of water resources, but nonstationarity skewness time series can pose major challenges for developing appropriate models. To address these issues, this paper proposes novel hybrid model by introducing variational mode decomposition (VMD) Box–Cox transformation (BC) into Elman neural network (Elman), named VMD-BC-Elman model. First, observed is decomposed sub-time using VMD better frequency resolution. Second, input datasets are transformed normal distribution Box–Cox, as result, skewedness data removed, correlation between output variables enhanced. The proposed VMD-BC preprocessing technology expected to overcome problems arising from nonstationary skewed data. Finally, used simulate respective series. evaluated at Zhangjiashan, Zhuangtou Huaxian hydrological stations Wei River Basin China. performances compared with those single models (SVM, Elman), decomposition-based (VMD-SVM, VMD-Elman et al.) BC-based (BC-SVM BC-Elman) employing four metrics. results show that outperform models, performs best all considered an NSE greater than 0.95, R 0.98, NMSE less 4.7%, PBIAS 0.4% both training testing periods. study indicates satisfactory data-driven approach predict series, representing effective tool predicting