Multi-step learning rule for recurrent neural models: an application to time series forecasting

Multi-step prediction is a difficult task that has attracted increasing interest in recent years. It tries to achieve predictions several steps ahead into the future starting from current information. The interest in this work is the development of nonlinear neural models for the purpose of building multi-step time series prediction schemes. In that context, the most popular neural models are based on the traditional feedforward neural networks. However, this kind of model may present some disadvantages when a long-term prediction problem is formulated because they are trained to predict only the next sampling time. In this paper, a neural model based on a partially recurrent neural network is proposed as a better alternative. For the recurrent model, a learning phase with the purpose of long-term prediction is imposed, which allows to obtain better predictions of time series in the future. In order to validate the performance of the recurrent neural model to predict the dynamic behaviour of the series in the future, three different data time series have been used as study cases. An artificial data time series, the logistic map, and two real time series, sunspots and laser data. Models based on feedforward neural networks have also been used and compared against the proposed model. The results suggest than the recurrent model can help in improving the prediction accuracy.Publicad

A matrix-based approach to solving the inverse Frobenius–Perron problem using sequences of density functions of stochastically perturbed dynamical systems

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density

Identification of Stochastically Perturbed Autonomous Systems from Temporal Sequences of Probability Density Functions

The paper introduces a method for reconstructing one-dimensional iterated maps that are driven by an external control input and subjected to an additive stochastic perturbation, from sequences of probability density functions that are generated by the stochastic dynamical systems and observed experimentally

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