Artificial neural network learning of nonstationary behavior in time series

We refine and complement a previously-proposed artificial neural network method for learning hidden signals forcing nonstationary behavior in time series. The method adds an extra input unit to the network and feeds it with the proposed profile for the unknown perturbing signal. The correct time evolution of this new input parameter is learned simultaneously with the intrinsic stationary dynamics underlying the series, which is accomplished by minimizing a suitably-defined error function for the training process. We incorporate here the use of validation data, held out from the training set, to accurately determine the optimal value of a hyperparameter required by the method. Furthermore, we evaluate this algorithm in a controlled situation and show that it outperforms other existing methods in the literature. Finally, we discuss a preliminary application to the real-world sunspot time series and link the obtained hidden perturbing signal to the secular evolution of the solar magnetic field.