Analysis and prediction of multivariate time series with networks and reservoir computing

The development of tools for characterizing current and predicting future states of higher-dimensional, complex dynamical systems is of great importance for both basic research and numerous applications. In this talk we will present two different approaches for assessing and predicting multivariate nonlinear time series. First we show how network analyses based on (non-)linear similarity measures can give very detailed insights into the correlation topology of the time series and their changes in time. Using examples from econophysics we outline the potential for forecasting future developments. Second we demonstrate how the the short and long term behavior of nonlinear dynamical systems can be reproduced by means of reservoir computing (RC). The influence of changes of the topology of the reservoir on the predictions quality is studied in detail. Current and future applications of RC are briefly discussed