Pronóstico de series temporales caoticas ruidosas aproximado mediante la combinación de la entropía de Reny con el método energía asociada a la serie: aplicación a las series de lluvia (Noisy Chaotic time series forecast approximated by combining Reny's entropy with Energy associated to series method: application to rainfall series)

Cristian Rodriguez Rivero (crodriguezrivero@ieee.org)1, Julian Pucheta (jpucheta@unc.edu.ar)1, Alvaro Orjuela Cañón (dorjuelac@gmail.com)2, Leonardo Franco (lfranco@lcc.uma.es)3, Yvan Tupac Valdivia (yvantv@ieee.org)4, Paula Otaño (paula.otano@gmail.com)5, Victor Sauchelli (victorsauchelli@gmail.com)1


1Universidad Nacional de Cordoba
2Universidad Antonio Nariño
3Universidad de Malaga
4Universidad Católica San Pablo
5Universidad Tecnologica Nacional

This paper appears in: Revista IEEE América Latina

Publication Date: July 2017
Volume: 15,   Issue: 7 
ISSN: 1548-0992


Abstract:
This article proposes that the combination of smoothing approach considering the entropic information provided by Renyi's method, has an acceptable performance in term of forecasting errors. The methodology of the proposed scheme is examined through benchmark chaotic time series, such as Mackey Glass, Lorenz, Henon maps, the Lynx and rainfall from Santa Francisca - Cordoba, with addition of white noise by using neural networks-based energy associated (EAS) predictor filter modified by Renyi's entropy of the series. When the time series is short or long, the underlying dynamical system is nonlinear and temporal dependencies span long time intervals, in which this are also called long memory process. In such cases, the inherent nonlinearity of neural networks models and a higher robustness to noise seem to partially explain their better prediction performance when entropic information is extracted from the series. Then, to demonstrate that permutation entropy is computationally efficient, robust to outliers, and effective to measure complexity of time series, computational results are evaluated against several non-linear ANN predictors to show the predictability of noisy rainfall and chaotic time series reported in the literature.

Index Terms:
neural networks, noisy chaotic time series, forecasting, energy associated to series (EAS), Renyi’s entropic information   


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