Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena ge...

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Autores principales:	Maria C. Mariani, William Kubin, Peter K. Asante, Joe A. Guthrie, Osei K. Tweneboah
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Cantor set fractals homeomorphism detrended fluctuation analysis Hurst exponent Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/f3d92cf3fb314ae0932fef09426a9c00
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id	oai:doaj.org-article:f3d92cf3fb314ae0932fef09426a9c00
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spelling	oai:doaj.org-article:f3d92cf3fb314ae0932fef09426a9c002021-11-25T17:30:20ZRelationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set10.3390/e231115051099-4300https://doaj.org/article/f3d92cf3fb314ae0932fef09426a9c002021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1505https://doaj.org/toc/1099-4300In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.Maria C. MarianiWilliam KubinPeter K. AsanteJoe A. GuthrieOsei K. TweneboahMDPI AGarticleCantor setfractalshomeomorphismdetrended fluctuation analysisHurst exponentScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1505, p 1505 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Cantor set fractals homeomorphism detrended fluctuation analysis Hurst exponent Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	Cantor set fractals homeomorphism detrended fluctuation analysis Hurst exponent Science Q Astrophysics QB460-466 Physics QC1-999 Maria C. Mariani William Kubin Peter K. Asante Joe A. Guthrie Osei K. Tweneboah Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
description	In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.
format	article
author	Maria C. Mariani William Kubin Peter K. Asante Joe A. Guthrie Osei K. Tweneboah
author_facet	Maria C. Mariani William Kubin Peter K. Asante Joe A. Guthrie Osei K. Tweneboah
author_sort	Maria C. Mariani
title	Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
title_short	Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
title_full	Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
title_fullStr	Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
title_full_unstemmed	Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
title_sort	relationship between continuum of hurst exponents of noise-like time series and the cantor set
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f3d92cf3fb314ae0932fef09426a9c00
work_keys_str_mv	AT mariacmariani relationshipbetweencontinuumofhurstexponentsofnoiseliketimeseriesandthecantorset AT williamkubin relationshipbetweencontinuumofhurstexponentsofnoiseliketimeseriesandthecantorset AT peterkasante relationshipbetweencontinuumofhurstexponentsofnoiseliketimeseriesandthecantorset AT joeaguthrie relationshipbetweencontinuumofhurstexponentsofnoiseliketimeseriesandthecantorset AT oseiktweneboah relationshipbetweencontinuumofhurstexponentsofnoiseliketimeseriesandthecantorset
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Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

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