Asymmetric Tsallis distributions for modeling financial market dynamics.
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| Title: | Asymmetric Tsallis distributions for modeling financial market dynamics. |
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| Authors: | Devi, Sandhya1 (AUTHOR) sdevi@entropicdynamics.com |
| Source: | Physica A. Sep2021, Vol. 578, pN.PAG-N.PAG. 1p. |
| Subjects: | Distribution (Probability theory), Financial markets, Rate of return on stocks, Data distribution, Nonlinear systems |
| Abstract: | Financial markets are highly non-linear and non-equilibrium systems. Earlier works have suggested that the behavior of market returns can be well described within the framework of non-extensive Tsallis statistics or superstatistics. For small time scales (delays), a good fit to the distributions of stock returns is obtained with q -Gaussian distributions, which can be derived either from Tsallis statistics or superstatistics. These distributions are symmetric. However, as the time lag increases, the distributions become increasingly non-symmetric. In this work, we address this problem by considering the data distribution as a linear combination of two independent normalized distributions — one for negative returns and one for positive returns. Each of these two independent distributions are half q -Gaussians with different non-extensivity parameter q and temperature parameter beta. Using this model, we investigate the behavior of stock market returns over time scales from 1 to 80 days. The data covers both the.com bubble and the 2008 crash periods. These investigations show that for all the time lags, the fits to the data distributions are better using asymmetric distributions than symmetric q -Gaussian distributions. The behaviors of the q parameter are quite different for positive and negative returns. For positive returns, q approaches a constant value of 1 after a certain lag, indicating the distributions have reached equilibrium. On the other hand, for negative returns, the q values do not reach a stationary value over the time scales studied. In the present model, the markets show a transition from normal to superdiffusive behavior (a possible phase transition) during the 2008 crash period. Such behavior is not observed with a symmetric q -Gaussian distribution model with q independent of time lag. [ABSTRACT FROM AUTHOR] |
| Copyright of Physica A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 150770567 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Asymmetric Tsallis distributions for modeling financial market dynamics. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Devi%2C+Sandhya%22">Devi, Sandhya</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sdevi@entropicdynamics.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Physica+A%22">Physica A</searchLink>. Sep2021, Vol. 578, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Financial+markets%22">Financial markets</searchLink><br /><searchLink fieldCode="DE" term="%22Rate+of+return+on+stocks%22">Rate of return on stocks</searchLink><br /><searchLink fieldCode="DE" term="%22Data+distribution%22">Data distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Financial markets are highly non-linear and non-equilibrium systems. Earlier works have suggested that the behavior of market returns can be well described within the framework of non-extensive Tsallis statistics or superstatistics. For small time scales (delays), a good fit to the distributions of stock returns is obtained with q -Gaussian distributions, which can be derived either from Tsallis statistics or superstatistics. These distributions are symmetric. However, as the time lag increases, the distributions become increasingly non-symmetric. In this work, we address this problem by considering the data distribution as a linear combination of two independent normalized distributions — one for negative returns and one for positive returns. Each of these two independent distributions are half q -Gaussians with different non-extensivity parameter q and temperature parameter beta. Using this model, we investigate the behavior of stock market returns over time scales from 1 to 80 days. The data covers both the.com bubble and the 2008 crash periods. These investigations show that for all the time lags, the fits to the data distributions are better using asymmetric distributions than symmetric q -Gaussian distributions. The behaviors of the q parameter are quite different for positive and negative returns. For positive returns, q approaches a constant value of 1 after a certain lag, indicating the distributions have reached equilibrium. On the other hand, for negative returns, the q values do not reach a stationary value over the time scales studied. In the present model, the markets show a transition from normal to superdiffusive behavior (a possible phase transition) during the 2008 crash period. Such behavior is not observed with a symmetric q -Gaussian distribution model with q independent of time lag. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Physica A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.physa.2021.126109 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Distribution (Probability theory) Type: general – SubjectFull: Financial markets Type: general – SubjectFull: Rate of return on stocks Type: general – SubjectFull: Data distribution Type: general – SubjectFull: Nonlinear systems Type: general Titles: – TitleFull: Asymmetric Tsallis distributions for modeling financial market dynamics. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Devi, Sandhya IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 09 Text: Sep2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 03784371 Numbering: – Type: volume Value: 578 Titles: – TitleFull: Physica A Type: main |
| ResultId | 1 |
