Ambiguities in Bandt-Pompes methodology for local entropic quantifiers
The BandtPompe (BP) prescription for building up probability densities [C. Bandt, B. Pompe, Permutation entropy: a natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102] constituted a significant advance in the treatment of time-series. However, as we show here, ambiguities a...
| Publicado: |
2012
|
|---|---|
| Materias: | |
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v391_n8_p2518_Olivares http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2518_Olivares |
| Aporte de: |
| id |
paper:paper_03784371_v391_n8_p2518_Olivares |
|---|---|
| record_format |
dspace |
| spelling |
paper:paper_03784371_v391_n8_p2518_Olivares2023-06-08T15:40:16Z Ambiguities in Bandt-Pompes methodology for local entropic quantifiers BandtPompe probability distribution Fisher information measure Nonlinear time series analysis Shannon entropy Complexity measures Fisher information measures Illustrative examples Nonlinear time series analysis Ordinal pattern Permutation entropy Probability densities Shannon entropy Fisher information matrix Nonlinear dynamical systems Probability density function Probability distributions Time series analysis The BandtPompe (BP) prescription for building up probability densities [C. Bandt, B. Pompe, Permutation entropy: a natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102] constituted a significant advance in the treatment of time-series. However, as we show here, ambiguities arise in applying the BP technique with reference to the permutation of ordinal patterns. This happens if one wishes to employ the BP-probability density to construct local entropic quantifiers that would characterize time-series generated by nonlinear dynamical systems. Explicit evidence of this fact is presented by comparing two different procedures, frequently found in the literature, that generate sequences of ordinal patterns. In opposition to the case of global quantifiers in the orthodox Shannon fashion, the proper order of the pertinent symbols turns out to be not uniquely predetermined for local entropic indicators. We advance the idea of employing the FisherShannon information plane as a tool to resolve the ambiguity and give illustrative examples. © 2011 Elsevier B.V. All rights reserved. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v391_n8_p2518_Olivares http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2518_Olivares |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
BandtPompe probability distribution Fisher information measure Nonlinear time series analysis Shannon entropy Complexity measures Fisher information measures Illustrative examples Nonlinear time series analysis Ordinal pattern Permutation entropy Probability densities Shannon entropy Fisher information matrix Nonlinear dynamical systems Probability density function Probability distributions Time series analysis |
| spellingShingle |
BandtPompe probability distribution Fisher information measure Nonlinear time series analysis Shannon entropy Complexity measures Fisher information measures Illustrative examples Nonlinear time series analysis Ordinal pattern Permutation entropy Probability densities Shannon entropy Fisher information matrix Nonlinear dynamical systems Probability density function Probability distributions Time series analysis Ambiguities in Bandt-Pompes methodology for local entropic quantifiers |
| topic_facet |
BandtPompe probability distribution Fisher information measure Nonlinear time series analysis Shannon entropy Complexity measures Fisher information measures Illustrative examples Nonlinear time series analysis Ordinal pattern Permutation entropy Probability densities Shannon entropy Fisher information matrix Nonlinear dynamical systems Probability density function Probability distributions Time series analysis |
| description |
The BandtPompe (BP) prescription for building up probability densities [C. Bandt, B. Pompe, Permutation entropy: a natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102] constituted a significant advance in the treatment of time-series. However, as we show here, ambiguities arise in applying the BP technique with reference to the permutation of ordinal patterns. This happens if one wishes to employ the BP-probability density to construct local entropic quantifiers that would characterize time-series generated by nonlinear dynamical systems. Explicit evidence of this fact is presented by comparing two different procedures, frequently found in the literature, that generate sequences of ordinal patterns. In opposition to the case of global quantifiers in the orthodox Shannon fashion, the proper order of the pertinent symbols turns out to be not uniquely predetermined for local entropic indicators. We advance the idea of employing the FisherShannon information plane as a tool to resolve the ambiguity and give illustrative examples. © 2011 Elsevier B.V. All rights reserved. |
| title |
Ambiguities in Bandt-Pompes methodology for local entropic quantifiers |
| title_short |
Ambiguities in Bandt-Pompes methodology for local entropic quantifiers |
| title_full |
Ambiguities in Bandt-Pompes methodology for local entropic quantifiers |
| title_fullStr |
Ambiguities in Bandt-Pompes methodology for local entropic quantifiers |
| title_full_unstemmed |
Ambiguities in Bandt-Pompes methodology for local entropic quantifiers |
| title_sort |
ambiguities in bandt-pompes methodology for local entropic quantifiers |
| publishDate |
2012 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v391_n8_p2518_Olivares http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2518_Olivares |
| _version_ |
1768541849648103424 |