Extracting driving signals from non-stationary time series

We propose a simple method for the reconstruction of slow dynamics perturbations from non-stationary time series records. The method traces the evolution of the perturbing signal by simultaneously learning the intrinsic stationary dynamics and the time dependency of the changing parameter. For this purpose, an extra input unit is added to a feedforward artificial neural network and a suitable error function minimized in the training process. Testing of our algorithm on synthetic data shows its efficacy and allows extracting general criteria for applications on real-world problems. Finally, a preliminary study of the well-known sunspot time series recovers particular features of this series, including recently reported changes in solar activity during last century.