17. Constraint-Based Neural Network Learning for Time Series Predictions

In this chapter, we have briefly surveyed previous work in predicting noise-free piecewise chaotic time series and noisy time series with high frequency random noise. For noise-free time series, we have proposed a constrained formulation for neural network learning that incorporates the error of each learning pattern as a constraint, a new cross-validation scheme that allows multiple validations sets to be considered in learning, a recurrent FIR neural network architecture that combines a recurrent structure and a memory-based FIR structure, and a violation-guided back propagation algorithm for searching in the constrained space of the formulation. For noisy time series, we have studied systematically the edge effect due to low-pass filtering of noisy time series and have developed an approach that incorporates constraints on predicting low-pass data in the lag period. The new constraints enable active training in the lag period that greatly improves the prediction accuracy in the lag period. Finally, experimental results show significant improvements in prediction accuracy on standard benchmarks and stock price time series.