DeepCascade-WR: a cascading deep architecture based on weak results for time series prediction

Noisy and nonstationary real-world time series predictions (TSPs) are challenging tasks. Confronted with these challenging tasks, the predictive power of traditional shallow models is commonly not satisfactory enough. While the research on deep learning (DL) has made milestone breakthrough in recent years, and DL paradigm has gradually become indispensable for accomplishing these complex tasks. In this work, a cascading deep architecture based on weak results (DeepCascade-WR) is established, which possesses deep models’ marked capability of feature representation learning based on complex data. In DeepCascade-WR, weak prediction results are defined, innovating the forecasting mode of traditional TSP. The original data will be properly reconstituted with prior knowledge, generating attribute vectors with valid predictive information. DeepCascade-WR possesses online learning ability and effectively avoids the retraining problem, owing to the property of OS-ELM, one base model of DeepCascade-WR. Besides, ELM is exploited as another base model of DeepCascade-WR, therefore, DeepCascade-WR naturally inherits some valuable virtues from ELM, including faster training speed, better generalization ability and the avoidance of being fallen into local optima. Ultimately, in the empirical results, DeepCascade-WR demonstrates its superior predictive performance on five benchmark financial datasets, i.e., ^DJI, ^GSK, ^HSI, JOUT, and S&P 500 Index, compared with its base learners and other state-of-the-art algorithms.