Correction to: Advanced series decomposition with a gated recurrent unit and graph convolutional neural network for non‑stationary data patterns

In this study, we present the EEG-GCN, a novel hybrid model for the prediction of time series data, adept at addressing the inherent challenges posed by the data's complex, non-linear, and periodic nature, as well as the noise that frequently accompanies it. This model synergizes signal decomposition techniques with a graph convolutional neural network (GCN) for enhanced analytical precision. The EEG-GCN approaches time series data as a one-dimensional temporal signal, applying a dual-layered signal decomposition using both Ensemble Empirical Mode Decomposition (EEMD) and GRU. This two-pronged decomposition process effectively eliminates noise interference and distills the complex signal into more tractable sub-signals. These sub-signals facilitate a more straightforward feature analysis and learning process. To capitalize on the decomposed data, a graph convolutional neural network (GCN) is employed to discern the intricate feature interplay within the sub-signals and to map the interdependencies among the data points. The predictive model then synthesizes the weighted outputs of the GCN to yield the final forecast. A key component of our approach is the integration of a Gated Recurrent Unit (GRU) with EEMD within the GCN framework, referred to as EEMD-GRU-GCN. This combination leverages the strengths of GRU in capturing temporal dependencies and the EEMD's capability in handling non-stationary data, thereby enriching the feature set available for the GCN and enhancing the overall predictive accuracy and stability of the model. Empirical evaluations demonstrate that the EEG-GCN model achieves superior performance metrics. Compared to the baseline GCN model, EEG-GCN shows an average R2 improvement of 60% to 90%, outperforming the other methods. These results substantiate the advanced predictive capability of our proposed model, underscoring its potential for robust and accurate time series forecasting.