An accurate algorithm to calculate the Hurst exponent of self-similar processes
In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst...
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| Veröffentlicht in: | Physics letters. A 2014-06, Vol.378 (32-33), p.2355-2362 |
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| container_title | Physics letters. A |
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| creator | Fernández-Martínez, M. Sánchez-Granero, M.A. Trinidad Segovia, J.E. Román-Sánchez, I.M. |
| description | In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered.
We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks.
•We provide a new approach to properly calculate the Hurst exponent.•This generalizes FD algorithms and GM2, introduced previously by the authors.•This method (FD4) results especially appropriate for short time series.•FD4 may be used in both unifractal and multifractal contexts.•As an empirical application, we show that S&P500 stocks improved their efficiency. |
| doi_str_mv | 10.1016/j.physleta.2014.06.018 |
| format | Article |
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We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks.
•We provide a new approach to properly calculate the Hurst exponent.•This generalizes FD algorithms and GM2, introduced previously by the authors.•This method (FD4) results especially appropriate for short time series.•FD4 may be used in both unifractal and multifractal contexts.•As an empirical application, we show that S&P500 stocks improved their efficiency.</description><identifier>ISSN: 0375-9601</identifier><identifier>EISSN: 1873-2429</identifier><identifier>DOI: 10.1016/j.physleta.2014.06.018</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Algorithms ; Dynamic tests ; Evolution ; Exponents ; FD algorithms ; Fractional Brownian motion ; GM algorithms ; Hurst exponent ; Long memory ; Lévy stable motion ; Mathematical analysis ; Raw materials ; Self-similarity ; Time series</subject><ispartof>Physics letters. A, 2014-06, Vol.378 (32-33), p.2355-2362</ispartof><rights>2014 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c415t-f1b841c1c1512db47b876f0471391c074472e918d6b359c851ea000fe36c3eb33</citedby><cites>FETCH-LOGICAL-c415t-f1b841c1c1512db47b876f0471391c074472e918d6b359c851ea000fe36c3eb33</cites><orcidid>0000-0001-9153-8321 ; 0000-0002-0098-4789 ; 0000-0001-6291-9205 ; 0000-0002-5017-2615</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.physleta.2014.06.018$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,778,782,3539,27907,27908,45978</link.rule.ids></links><search><creatorcontrib>Fernández-Martínez, M.</creatorcontrib><creatorcontrib>Sánchez-Granero, M.A.</creatorcontrib><creatorcontrib>Trinidad Segovia, J.E.</creatorcontrib><creatorcontrib>Román-Sánchez, I.M.</creatorcontrib><title>An accurate algorithm to calculate the Hurst exponent of self-similar processes</title><title>Physics letters. A</title><description>In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered.
We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks.
•We provide a new approach to properly calculate the Hurst exponent.•This generalizes FD algorithms and GM2, introduced previously by the authors.•This method (FD4) results especially appropriate for short time series.•FD4 may be used in both unifractal and multifractal contexts.•As an empirical application, we show that S&P500 stocks improved their efficiency.</description><subject>Algorithms</subject><subject>Dynamic tests</subject><subject>Evolution</subject><subject>Exponents</subject><subject>FD algorithms</subject><subject>Fractional Brownian motion</subject><subject>GM algorithms</subject><subject>Hurst exponent</subject><subject>Long memory</subject><subject>Lévy stable motion</subject><subject>Mathematical analysis</subject><subject>Raw materials</subject><subject>Self-similarity</subject><subject>Time series</subject><issn>0375-9601</issn><issn>1873-2429</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqFkMtOwzAQRS0EEqXwC8hLNgmexHGcHVXFS6rUDawtx5lQV84D20H070lVWKNZjDS6987MIeQWWAoMxP0-HXeH4DDqNGPAUyZSBvKMLECWeZLxrDonC5aXRVIJBpfkKoQ9Y7OTVQuyXfVUGzN5HZFq9zF4G3cdjQM12pnJHcdxh_Rl8iFS_B6HHvtIh5YGdG0SbGed9nT0g8EQMFyTi1a7gDe_fUnenx7f1i_JZvv8ul5tEsOhiEkLteRg5ioga2pe1rIULeMl5BUYVnJeZliBbESdF5WRBaCeb24xFybHOs-X5O6UO2_-nDBE1dlg0Dnd4zAFBUVRCSllxWapOEmNH0Lw2KrR2077gwKmjgTVXv0RVEeCigk1E5yNDycjzo98WfQqGIu9wcZ6NFE1g_0v4gdJ7n2O</recordid><startdate>20140627</startdate><enddate>20140627</enddate><creator>Fernández-Martínez, M.</creator><creator>Sánchez-Granero, M.A.</creator><creator>Trinidad Segovia, J.E.</creator><creator>Román-Sánchez, I.M.</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7QQ</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JG9</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0001-9153-8321</orcidid><orcidid>https://orcid.org/0000-0002-0098-4789</orcidid><orcidid>https://orcid.org/0000-0001-6291-9205</orcidid><orcidid>https://orcid.org/0000-0002-5017-2615</orcidid></search><sort><creationdate>20140627</creationdate><title>An accurate algorithm to calculate the Hurst exponent of self-similar processes</title><author>Fernández-Martínez, M. ; Sánchez-Granero, M.A. ; Trinidad Segovia, J.E. ; Román-Sánchez, I.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c415t-f1b841c1c1512db47b876f0471391c074472e918d6b359c851ea000fe36c3eb33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algorithms</topic><topic>Dynamic tests</topic><topic>Evolution</topic><topic>Exponents</topic><topic>FD algorithms</topic><topic>Fractional Brownian motion</topic><topic>GM algorithms</topic><topic>Hurst exponent</topic><topic>Long memory</topic><topic>Lévy stable motion</topic><topic>Mathematical analysis</topic><topic>Raw materials</topic><topic>Self-similarity</topic><topic>Time series</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fernández-Martínez, M.</creatorcontrib><creatorcontrib>Sánchez-Granero, M.A.</creatorcontrib><creatorcontrib>Trinidad Segovia, J.E.</creatorcontrib><creatorcontrib>Román-Sánchez, I.M.</creatorcontrib><collection>CrossRef</collection><collection>Ceramic Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics letters. A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fernández-Martínez, M.</au><au>Sánchez-Granero, M.A.</au><au>Trinidad Segovia, J.E.</au><au>Román-Sánchez, I.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An accurate algorithm to calculate the Hurst exponent of self-similar processes</atitle><jtitle>Physics letters. A</jtitle><date>2014-06-27</date><risdate>2014</risdate><volume>378</volume><issue>32-33</issue><spage>2355</spage><epage>2362</epage><pages>2355-2362</pages><issn>0375-9601</issn><eissn>1873-2429</eissn><abstract>In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered.
We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks.
•We provide a new approach to properly calculate the Hurst exponent.•This generalizes FD algorithms and GM2, introduced previously by the authors.•This method (FD4) results especially appropriate for short time series.•FD4 may be used in both unifractal and multifractal contexts.•As an empirical application, we show that S&P500 stocks improved their efficiency.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physleta.2014.06.018</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0001-9153-8321</orcidid><orcidid>https://orcid.org/0000-0002-0098-4789</orcidid><orcidid>https://orcid.org/0000-0001-6291-9205</orcidid><orcidid>https://orcid.org/0000-0002-5017-2615</orcidid></addata></record> |
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| ispartof | Physics letters. A, 2014-06, Vol.378 (32-33), p.2355-2362 |
| issn | 0375-9601 1873-2429 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Algorithms Dynamic tests Evolution Exponents FD algorithms Fractional Brownian motion GM algorithms Hurst exponent Long memory Lévy stable motion Mathematical analysis Raw materials Self-similarity Time series |
| title | An accurate algorithm to calculate the Hurst exponent of self-similar processes |
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