Forward Moving Average Representation in Multivariate MA(1) Processes

A Novel Broad Echo State Network for Time Series Prediction: Cascade of Mapping Nodes and Optimization of Enhancement Layer

Time series prediction is crucial for advanced control and management of complex systems, while the actual data are usually highly nonlinear and nonstationary. A novel broad echo state network is proposed herein for the prediction problem of complex time series data. Firstly, the framework of the broad echo state network with cascade of mapping nodes (CMBESN) is designed by embedding the echo state network units into the broad learning system. Secondly, the number of enhancement layer nodes of the CMBESN is determined by proposing an incremental algorithm. It can obtain the optimal network structure parameters. Meanwhile, an optimization method is proposed based on the nonstationary statistic metrics to determine the enhancement layer. Finally, experiments are conducted both on the simulated and actual datasets. The results show that the proposed CMBESN and its optimization have good prediction capability for nonstationary time series data.

Broad Echo State Network with Reservoir Pruning for Nonstationary Time Series Prediction

The nonstationary time series is generated in various natural and man-made systems, of which the prediction is vital for advanced control and management. The neural networks have been explored in the time series prediction, but the problem remains in modeling the data’s nonstationary and nonlinear features. Referring to the time series feature and network property, a novel network is designed with dynamic optimization of the model structure. Firstly, the echo state network (ESN) is introduced into the broad learning system (BLS). The broad echo state network (BESN) can increase the training efficiency with the incremental learning algorithm by removing the error backpropagation. Secondly, an optimization algorithm is proposed to reduce the redundant information in the training process of BESN units. The number of neurons in BESN with a fixed step size is pruned according to the contribution degree. Finally, the improved network is applied in the different datasets. The tests in the time series of natural and man-made systems prove that the proposed network performs better on the nonstationary time series prediction than the typical methods, including the ESN, BLS, and recurrent neural network.