Modeling Dynamical Systems by Error Correction Neural Networks

Abstract

We introduce a new time delay recurrent neural network called ECNN, which includes the last model error as an additional input. Hence, the learning can interpret the models misspecification as an external shock which can be used to guide the model dynamics afterwards. As extension to the ECNN, we present a concept called overshooting, which enforces the autoregressive part of the model and thus, allows long term forecasts. Modeling high-dimensional dynamical systems, we introduce the principle of variants-invariants separation, which simplifies the high-dimensional forecasting problem by a suitable coordinate transformation. Focusing on optimal state space reconstruction, we try to specify a transformation such that the related forecast problem becomes easier, i. e. it evolves more smoothly over time. Here, we propose an integrated neural network approach which combines state space reconstruction and forecasting. Finally we apply the ECNN to the complete German yield curve. Our model allows a forecast of ten different interest rate maturities on forecast horizons between one and six months ahead. It turns out, that our approach is superior to more conventional forecasting techniques.