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

Recurrent Neural Networks Applied to GNSS Time Series for Denoising and Prediction

Global Navigation Satellite Systems (GNSS) are systems that continuously acquire data and provide position time series. Many monitoring applications are based on GNSS data and their efficiency depends on the capability in the time series analysis to characterize the signal content and/or to predict incoming coordinates. In this work we propose a suitable Network Architecture, based on Long Short Term Memory Recurrent Neural Networks, to solve two main tasks in GNSS time series analysis: denoising and prediction. We carry out an analysis on a synthetic time series, then we inspect two real different case studies and evaluate the results. We develop a non-deep network that removes almost the 50% of scattering from real GNSS time series and achieves a coordinate prediction with 1.1 millimeters of Mean Squared Error