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Open AccessArticle

Time Series Complexities and Their Relationship to Forecasting Performance

Graduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Cd. Madero 89440, Mexico
Information Technologies Department, Consejo Nacional de Ciencia y Tecnología—Instituto Nacional de Electricidad y Energías Limpias, Cuernavaca 62490, Mexico
Computing Department, Tecnológico Nacional de México/Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca 62490, Mexico
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2020, 22(1), 89;
Received: 17 December 2019 / Revised: 6 January 2020 / Accepted: 7 January 2020 / Published: 10 January 2020
(This article belongs to the Special Issue Entropy Application for Forecasting)
Entropy is a key concept in the characterization of uncertainty for any given signal, and its extensions such as Spectral Entropy and Permutation Entropy. They have been used to measure the complexity of time series. However, these measures are subject to the discretization employed to study the states of the system, and identifying the relationship between complexity measures and the expected performance of the four selected forecasting methods that participate in the M4 Competition. This relationship allows the decision, in advance, of which algorithm is adequate. Therefore, in this paper, we found the relationships between entropy-based complexity framework and the forecasting error of four selected methods (Smyl, Theta, ARIMA, and ETS). Moreover, we present a framework extension based on the Emergence, Self-Organization, and Complexity paradigm. The experimentation with both synthetic and M4 Competition time series show that the feature space induced by complexities, visually constrains the forecasting method performance to specific regions; where the logarithm of its metric error is poorer, the Complexity based on the emergence and self-organization is maximal. View Full-Text
Keywords: classical forecasting methods; complexity; entropy; error measures; symbolic analysis; M4 competition classical forecasting methods; complexity; entropy; error measures; symbolic analysis; M4 competition
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Ponce-Flores, M.; Frausto-Solís, J.; Santamaría-Bonfil, G.; Pérez-Ortega, J.; González-Barbosa, J.J. Time Series Complexities and Their Relationship to Forecasting Performance. Entropy 2020, 22, 89.

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