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Information Theory for Non-Stationary Processes with Stationary Increments
We describe how to analyze the wide class of non-stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual infor...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514568/ http://dx.doi.org/10.3390/e21121223 |
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author | Granero-Belinchón, Carlos Roux, Stéphane G. Garnier, Nicolas B. |
author_facet | Granero-Belinchón, Carlos Roux, Stéphane G. Garnier, Nicolas B. |
author_sort | Granero-Belinchón, Carlos |
collection | PubMed |
description | We describe how to analyze the wide class of non-stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information, and entropy rate can be estimated when only a single realization of the process is available. We abundantly illustrate our approach by analyzing Gaussian and non-Gaussian self-similar signals, as well as multi-fractal signals. Using Gaussian signals allows us to check that our approach is robust in the sense that all quantities behave as expected from analytical derivations. Using the stationarity (independence on the integration time) of the ersatz entropy rate, we show that this quantity is not only able to fine probe the self-similarity of the process, but also offers a new way to quantify the multi-fractality. |
format | Online Article Text |
id | pubmed-7514568 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75145682020-11-09 Information Theory for Non-Stationary Processes with Stationary Increments Granero-Belinchón, Carlos Roux, Stéphane G. Garnier, Nicolas B. Entropy (Basel) Article We describe how to analyze the wide class of non-stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information, and entropy rate can be estimated when only a single realization of the process is available. We abundantly illustrate our approach by analyzing Gaussian and non-Gaussian self-similar signals, as well as multi-fractal signals. Using Gaussian signals allows us to check that our approach is robust in the sense that all quantities behave as expected from analytical derivations. Using the stationarity (independence on the integration time) of the ersatz entropy rate, we show that this quantity is not only able to fine probe the self-similarity of the process, but also offers a new way to quantify the multi-fractality. MDPI 2019-12-15 /pmc/articles/PMC7514568/ http://dx.doi.org/10.3390/e21121223 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Granero-Belinchón, Carlos Roux, Stéphane G. Garnier, Nicolas B. Information Theory for Non-Stationary Processes with Stationary Increments |
title | Information Theory for Non-Stationary Processes with Stationary Increments |
title_full | Information Theory for Non-Stationary Processes with Stationary Increments |
title_fullStr | Information Theory for Non-Stationary Processes with Stationary Increments |
title_full_unstemmed | Information Theory for Non-Stationary Processes with Stationary Increments |
title_short | Information Theory for Non-Stationary Processes with Stationary Increments |
title_sort | information theory for non-stationary processes with stationary increments |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514568/ http://dx.doi.org/10.3390/e21121223 |
work_keys_str_mv | AT granerobelinchoncarlos informationtheoryfornonstationaryprocesseswithstationaryincrements AT rouxstephaneg informationtheoryfornonstationaryprocesseswithstationaryincrements AT garniernicolasb informationtheoryfornonstationaryprocesseswithstationaryincrements |