Input-output model of time series based on ESN

Echo state networks (ESN) is a novel time series model stemming from RNN. The reservoir of ESN provides a rich set of dynamics whose weighted combination can approximate teacher signal effectively. Its excellent predicting capability in deterministic system has been proved by several benchmarks. Yet analyzing an input-output system using ESN has not discussed. In the paper a new I/O model is presented to address both input and output series as the observation of systems which comprise a teacher vector. Learning the vector by ESN can establish the mapping from input to output and predict the system output on the basis of new input. Though learning only the output series can also predict the unknown quantity, repeating simulations demonstrate that our model can restrain the instability of network state and improve the predicting performance. Such model gives us new choice to analyze input-output system.