Noisy Chaotic time series forecast approximated by combining Reny's entropy with Energy associated to series method: application to rainfall series

• Published in: Revista IEEE América Latina Vol. 15; no. 7; pp. 1318 - 1325
• Main Authors: Rodriguez Rivero, Cristian, Pucheta, Julian, Orjuela Canon, Alvaro, Franco, Leonardo, Tupac Valdivia, Yvan, Otano, Paula, Sauchelli, Victor
• Format: Journal Article
• Language: English
• Published: Los Alamitos IEEE 2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Benchmark testing; Chaos theory; Complexity; Computational modeling; energy associated to series (EAS); Energy consumption; Entropy; Entropy (Information theory); forecasting; Information dissemination; Neural networks; Noise measurement; Noise prediction; noisy chaotic time series; Nonlinearity; Outliers (statistics); Rainfall; Renyi's entropic information; RNA; Robustness; Robustness (mathematics); Smoothing; Time measurement; Time series; Time series analysis; White noise
• ISSN: 1548-0992; 1548-0992
• DOI: 10.1109/TLA.2017.7959353

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.