Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series

ilustraciones a color, diagramas

Autores:
Abril Bermúdez, Felipe Segundo
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2024
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
OAI Identifier:
oai:repositorio.unal.edu.co:unal/85513
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/85513
https://repositorio.unal.edu.co/
Palabra clave:
530 - Física::539 - Física moderna
330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Multifractal system
Supersymmetry
Fractional calculus
Análisis multifractal
Supersimetría
Cálculo fraccionario
Movimiento browniano
Análisis de series de tiempo
Procesos estocásticos
Brownian movements
Time-series analysis
Stochastic processes
Fractional stochastic path integral formalism
Fractional Brownian motion
Econophysics
Multifractality
Shannon index
Supersymmetric theory of stochastic dynamics
Formalismo de integral de camino estocástica fraccional
Movimiento Browniano fraccional
Econofísica
Multifractalidad
Índice de Shannon
Teoría supersimétrica de la dinámica estocástica
Econofísica
Econophysics
Rights
openAccess
License
Atribución-CompartirIgual 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/85513
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.eng.fl_str_mv Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
dc.title.translated.spa.fl_str_mv Movimiento Browniano fraccional aplicado al estudio de la dinámica asociada con series de tiempo no estacionarias
title Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
spellingShingle Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
530 - Física::539 - Física moderna
330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Multifractal system
Supersymmetry
Fractional calculus
Análisis multifractal
Supersimetría
Cálculo fraccionario
Movimiento browniano
Análisis de series de tiempo
Procesos estocásticos
Brownian movements
Time-series analysis
Stochastic processes
Fractional stochastic path integral formalism
Fractional Brownian motion
Econophysics
Multifractality
Shannon index
Supersymmetric theory of stochastic dynamics
Formalismo de integral de camino estocástica fraccional
Movimiento Browniano fraccional
Econofísica
Multifractalidad
Índice de Shannon
Teoría supersimétrica de la dinámica estocástica
Econofísica
Econophysics
title_short Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
title_full Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
title_fullStr Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
title_full_unstemmed Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
title_sort Fractional Brownian motion applied to the study of the dynamics associated with non-stationary time series
dc.creator.fl_str_mv Abril Bermúdez, Felipe Segundo
dc.contributor.advisor.none.fl_str_mv Quimbay Herrera, Carlos José
dc.contributor.author.none.fl_str_mv Abril Bermúdez, Felipe Segundo
dc.contributor.researchgroup.spa.fl_str_mv Econofisica y Sociofisica
dc.contributor.orcid.spa.fl_str_mv Felipe Segundo Abril Bermúdez [0000-0002-2512-4929]
dc.contributor.cvlac.spa.fl_str_mv Felipe Segundo Abril Bermúdez
dc.contributor.researchgate.spa.fl_str_mv Felipe Segundo Abril Bermúdez
dc.contributor.googlescholar.spa.fl_str_mv Felipe Segundo Abril Bermúdez
dc.subject.ddc.spa.fl_str_mv 530 - Física::539 - Física moderna
330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
topic 530 - Física::539 - Física moderna
330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Multifractal system
Supersymmetry
Fractional calculus
Análisis multifractal
Supersimetría
Cálculo fraccionario
Movimiento browniano
Análisis de series de tiempo
Procesos estocásticos
Brownian movements
Time-series analysis
Stochastic processes
Fractional stochastic path integral formalism
Fractional Brownian motion
Econophysics
Multifractality
Shannon index
Supersymmetric theory of stochastic dynamics
Formalismo de integral de camino estocástica fraccional
Movimiento Browniano fraccional
Econofísica
Multifractalidad
Índice de Shannon
Teoría supersimétrica de la dinámica estocástica
Econofísica
Econophysics
dc.subject.lcc.eng.fl_str_mv Multifractal system
Supersymmetry
Fractional calculus
dc.subject.lcc.spa.fl_str_mv Análisis multifractal
Supersimetría
Cálculo fraccionario
dc.subject.lemb.spa.fl_str_mv Movimiento browniano
Análisis de series de tiempo
Procesos estocásticos
dc.subject.lemb.eng.fl_str_mv Brownian movements
Time-series analysis
Stochastic processes
dc.subject.proposal.eng.fl_str_mv Fractional stochastic path integral formalism
Fractional Brownian motion
Econophysics
Multifractality
Shannon index
Supersymmetric theory of stochastic dynamics
dc.subject.proposal.spa.fl_str_mv Formalismo de integral de camino estocástica fraccional
Movimiento Browniano fraccional
Econofísica
Multifractalidad
Índice de Shannon
Teoría supersimétrica de la dinámica estocástica
dc.subject.wikidata.spa.fl_str_mv Econofísica
dc.subject.wikidata.eng.fl_str_mv Econophysics
description ilustraciones a color, diagramas
publishDate 2024
dc.date.accessioned.none.fl_str_mv 2024-01-30T15:09:12Z
dc.date.available.none.fl_str_mv 2024-01-30T15:09:12Z
dc.date.issued.none.fl_str_mv 2024-01-29
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/85513
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/85513
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv eng
language eng
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spelling Atribución-CompartirIgual 4.0 Internacionalhttp://creativecommons.org/licenses/by-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Quimbay Herrera, Carlos José8085b0115e03c75c6f713b3beab55a6a600Abril Bermúdez, Felipe Segundoc283cecd72678587dc9ea4eda9e9f1a5Econofisica y SociofisicaFelipe Segundo Abril Bermúdez [0000-0002-2512-4929]Felipe Segundo Abril BermúdezFelipe Segundo Abril BermúdezFelipe Segundo Abril Bermúdez2024-01-30T15:09:12Z2024-01-30T15:09:12Z2024-01-29https://repositorio.unal.edu.co/handle/unal/85513Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones a color, diagramasEn esta tesis doctoral se propone extender los procesos fraccionales estables, como el movimiento browniano fraccionario, haciendo uso del formalismo de la integral de camino de tal manera que tenga asociada una distribución de Levy truncada, estableciendo un vínculo entre el exponente de Hurst y el exponente del escalamiento temporal de Theil, y verificando este vínculo en series de tiempo no estacionarias empíricas. Para ello, como punto de referencia de la correcta construcción de una integral de camino estocástica, se propone primero explicar la existencia del escalamiento de la fluctuación temporal y la variación temporal de su exponente introduciendo una contribución estocástica dependiente del tiempo en la función generadora de cumulantes de la probabilidad de transición entre dos tiempos de una variable estocástica descrita en términos de un kernel de Feynman. Así, la función generadora de cumulantes se identifica como el hamiltoniano del sistema y la integral de trayectoria estocástica se inscribe en el contexto de la teoría supersimétrica de la dinámica estocástica. Con base en estos resultados y utilizando el índice de Shannon, se encuentra un nuevo escalamiento temporal denominado escalamiento temporal del índice de Theil en series de tiempo de trayectorias difusivas. De hecho, la existencia del escalamiento temporal del Theil se muestra en una amplia variedad de series de tiempo empíricas que utilizan el algoritmo de trayectoria difusiva. Además, el escalamiento temporal del Theil puede describirse como una transición de fase asociada con un funcional de energía con exponentes fraccionales y con un parámetro de orden asociado con el índice de Shannon normalizado a su valor máximo. Luego, se investiga la dependencia del exponente de Hurst generalizado con el exponente del escalamiento temporal del Theil en series de tiempo, estableciendo una relación teórica desde el enfoque de la función de partición multifractal. Finalmente, la generalización de la fórmula de Feynman-Kac se realiza en procesos fraccionales estables independiente del tipo de ruido subyacente en el sistema y teniendo en cuenta el formalismo de la integral de camino estocástica. Así, el formalismo de la integral de camino estocástica fraccional se define en términos de la función generadora de cumulantes del ruido del sistema y se aplica al caso particular de una distribución de Levy truncada. (Texto tomado de la fuente)In this doctoral thesis, it is proposed to extend the fractional stable processes, such as the fractional Brownian motion, making use of the path integral formalism in such a way that they have an associated truncated Levy distribution, establishing a link between the Hurst exponent and the temporal Theil scaling exponent and verifying this link in non-stationary empirical time series. To do this, as a benchmark of the correct construction of a stochastic path integral, it is first proposed to explain the existence of the temporal fluctuation scaling and the temporal variation of its exponent by introducing a time-dependent stochastic contribution in the cumulant generating function of the probability of change between two times of a stochastic variable described in terms of a Feynman kernel. Thus, the cumulant generating function is identified as the Hamiltonian of the system and the stochastic path integral is inscribed in the context of the supersymmetric theory of stochastic dynamics. Based on these results and using the Shannon index, a new time scaling called temporal Theil scaling is found in time series of diffusive trajectories. Indeed, the existence of temporal Theil scaling is shown in a wide variety of empirical time series using the diffusive path algorithm. Furthermore, the temporal Theil scaling can be described as a phase transition associated with an energy functional with fractional exponents and with an order parameter associated with the Shannon index normalized to its maximum value. Then, the temporal dependence of the generalized Hurst exponent with the temporal Theil scaling exponent in time series is investigated, establishing a theoretical relationship from the multifractal partition function approach. Finally, the generalization of the Feynman-Kac formula is made in fractional stable processes independent of the type of underlying noise in the system and taking into account the formalism of the stochastic path integral. Thus, the formalism of the fractional stochastic path integral is defined in terms of the cumulant generating function of the noise of the system and it is applied to the particular case of a truncated Levy distribution.DoctoradoDoctor en Ciencias - Físicaxviii, 160 páginasapplication/pdfengDepartamento de Física - Universidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - FísicaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá530 - Física::539 - Física moderna330 - Economía::332 - Economía financiera510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasMultifractal systemSupersymmetryFractional calculusAnálisis multifractalSupersimetríaCálculo fraccionarioMovimiento brownianoAnálisis de series de tiempoProcesos estocásticosBrownian movementsTime-series analysisStochastic processesFractional stochastic path integral formalismFractional Brownian motionEconophysicsMultifractalityShannon indexSupersymmetric theory of stochastic dynamicsFormalismo de integral de camino estocástica fraccionalMovimiento Browniano fraccionalEconofísicaMultifractalidadÍndice de ShannonTeoría supersimétrica de la dinámica estocásticaEconofísicaEconophysicsFractional Brownian motion applied to the study of the dynamics associated with non-stationary time seriesMovimiento Browniano fraccional aplicado al estudio de la dinámica asociada con series de tiempo no estacionariasTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDF. S. Abril and C. J. Quimbay. Temporal fluctuation scaling in non-stationary time series using the path integral formalism. Phys. Rev. E, 103(4), 04 2021. doi: https://doi.org/10.1103/PhysRevE.103.042126.F. S. Abril and C. J. Quimbay. Temporal Theil scaling in diffusive trajectory time series. Phys. Rev. E, 106(1), 07 2022. doi: https://doi.org/10.1103/PhysRevE.106.014117.F. S. Abril and C. J. Quimbay. Evolution of temporal fluctuation scaling exponent in nonstationary time series using supersymmetric theory of stochastic dynamics. Manuscript accepted to be published on Phys. Rev. E at: https://journals.aps.org/pre/accepted/02074Rb1Xe31ac2a727e1f49be6f73c21dba65baf, 01 2024.F. S. Abril and C. J. Quimbay. Temporal fluctuation scaling and temporal Theil scaling in financial time series. In Advances in quantitative methods for economics and business. Springer, 07 2024. Manuscript accepted to be published as a chapter (forthcoming).F. S. Abril, J. E. Trinidad-Segovia, M. A. 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Rev., 83(3):678–679, 08 1951. doi: https://doi.org/10.1103/PhysRev.83.678.EstudiantesInvestigadoresORIGINAL1013671689.2023.pdf1013671689.2023.pdfTesis de Doctorado en Físicaapplication/pdf20373904https://repositorio.unal.edu.co/bitstream/unal/85513/2/1013671689.2023.pdfe83a4ec8f62fbc318c2c7c9142838c13MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/85513/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53THUMBNAIL1013671689.2023.pdf.jpg1013671689.2023.pdf.jpgGenerated Thumbnailimage/jpeg7452https://repositorio.unal.edu.co/bitstream/unal/85513/4/1013671689.2023.pdf.jpg513979382778f13f7f15cdea533ff5a7MD54unal/85513oai:repositorio.unal.edu.co:unal/855132024-01-30 23:03:50.576Repositorio Institucional Universidad Nacional de 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