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HP-ESN: Echo State Networks Combined with Hodrick-Prescott Filter for Nonlinear Time-Series Prediction

Nonlinear time-series prediction is one of the challenging tasks in machine learning. Recurrent neural networks and their variants have been successful in such a task owing to its ability of storing past inputs in their dynamical states. Echo state networks (ESNs) are a special type of recurrent neural networks, which are capable of high-speed learning. To develop this computational scheme, we propose an HP-ESN method which combines ESNs with a preprocessing based on the Hodrick- Prescott (HP) filter. This filter extracts different components from a single time-series data. The extracted components are processed by ESNs. We show that the proposed method yields better prediction performance compared with other state-of- the-art ESN-based methods in prediction tasks with real-world time-series data. We also demonstrate that the computational performance depends on the setting of the smoothing parameter and the number of decompositions by the HP filter.