Propuesta de un modelo estadístico para estimar la volatilidad estocástica de un activo financiero usando un modelo de filtrado de partículas basado en wavelets
| dc.contributor.advisor | Hernández Barajas, Freddy | |
| dc.contributor.author | Rios Saavedra, Omar Alexander | |
| dc.contributor.orcid | Rios Saavedra, Omar Alexander [0009000771651467] | |
| dc.contributor.orcid | Hernández-Barajas, Freddy [0000000174593329] | |
| dc.date.accessioned | 2025-12-01T20:02:06Z | |
| dc.date.available | 2025-12-01T20:02:06Z | |
| dc.date.issued | 2025-11-27 | |
| dc.description.abstract | Este trabajo desarrolla un algoritmo de contracción de coeficientes wavelets (Wavelet Shrinkage) con el objetivo de eliminar ruido aditivo en series de tiempo que presentan un erroraleatorio inherente. El algoritmo propuesto, denominado BayeShrinkPL, se basa en un enfoque bayesiano de aprendizaje de partículas que constituye un caso particular de los métodos secuenciales Monte Carlo. Este método de eliminación de ruido mediante wavelets se integra dentro del algoritmo de filtrado de partículas, dando lugar a una nueva propuesta de estimación basada en empujes wavelet que se denomina NuWPF. Este enfoque es usado para el cálculo de la volatilidad estocástica de un activo financiero. Adicionalmente, también se propone la implementación del enfoque BayeShrinkPL en el algoritmo Liu & West para estimar la volatilidad latente y sus parámetros. A esta metodología se denomina NuWLW. Los resultados muestran que el método BayeShrinkPL es más eficiente en la eliminación de ruido comparado con los métodos convencionales. Así mismo, los enfoques NuWPF y NuWLW lograron mejorar el ajuste en la estimación de la volatilidad estocástica en comparación con los métodos tradicionales como el filtro auxiliar de partículas (APF) y el algoritmo Liu & West (LW) estándar (Tomado de la fuene) | spa |
| dc.description.abstract | This thesis work develops a wavelet coefficient shrinkage algorithm (Wavelet Shrinkage) aimed at removing additive noise in time series characterized by inherent random error. The proposed algorithm, denoted as BayeShrinkPL, is based on a Bayesian particle learning approach, which represents a particular case of sequential Monte Carlo methods. This wavelet-based noise removal method technique is incorporated within the particle filtering algorithm, resulting in a novel estimation approach based on wavelet nudging termed NuWPF. This approach is used to calculate the stochastic volatility of a financial asset. Additionally, the implementation of the BayeShrinkPL approach is also proposed within the Liu & West algorithm to estimate latent volatility and its parameters. This methodology is denoted as NuWLW. The results indicate that the BayeShrinkPL method is more efficient in noise removal compared to conventional methods. Furthermore, the NuWPF and NuWLW approaches achieved improved fit in the estimation of stochastic volatility compared to traditional methods such as the auxiliary particle filter (APF) and the standard Liu & West (LW) algorithm. | eng |
| dc.description.curriculararea | Estadística.Sede Medellín | |
| dc.description.degreelevel | Doctorado | |
| dc.description.degreename | Doctor en Ciencias - Estadística | |
| dc.format.extent | 1 recurso en línea (167 páginas) | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.instname | Universidad Nacional de Colombia | spa |
| dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia | spa |
| dc.identifier.repourl | https://repositorio.unal.edu.co/ | spa |
| dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/89168 | |
| dc.language.iso | spa | |
| dc.publisher | Universidad Nacional de Colombia | |
| dc.publisher.branch | Universidad Nacional de Colombia - Sede Medellín | |
| dc.publisher.faculty | Facultad de Ciencias | |
| dc.publisher.place | Medellín, Colombia | |
| dc.publisher.program | Medellín - Ciencias - Doctorado en Ciencias - Estadística | |
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| dc.rights.accessrights | info:eu-repo/semantics/openAccess | |
| dc.rights.license | Reconocimiento 4.0 Internacional | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject.ddc | 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas | |
| dc.subject.lemb | Procesos estocasticos | |
| dc.subject.lemb | Métdodo de Montecarlo | |
| dc.subject.proposal | Volatilidad estocástica | spa |
| dc.subject.proposal | Métodos secuenciales Monte Carlo | spa |
| dc.subject.proposal | Filtro de partículas basado en wavelets | spa |
| dc.subject.proposal | Shrinkage Bayesiano | spa |
| dc.subject.proposal | Aprendizaje de partículas, | spa |
| dc.subject.proposal | Filtro de partículas | spa |
| dc.subject.proposal | Stochastic Volatility | eng |
| dc.subject.proposal | Sequential Monte Carlo Method, | eng |
| dc.subject.proposal | Wavelet-based particle filter | eng |
| dc.subject.proposal | Bayesian shrinkage | eng |
| dc.subject.proposal | Particle learning | eng |
| dc.subject.proposal | Particle filter | eng |
| dc.subject.wikidata | Estadística bayesiana | |
| dc.title | Propuesta de un modelo estadístico para estimar la volatilidad estocástica de un activo financiero usando un modelo de filtrado de partículas basado en wavelets | spa |
| dc.title.translated | Proposal for a statistical model to estimate the stochastic volatility of a financial asset using a wavelet-based particle filtering model | eng |
| dc.type | Trabajo de grado - Doctorado | |
| dc.type.coar | http://purl.org/coar/resource_type/c_db06 | |
| dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | |
| dc.type.content | Text | |
| dc.type.driver | info:eu-repo/semantics/doctoralThesis | |
| dc.type.redcol | http://purl.org/redcol/resource_type/TD | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dcterms.audience.professionaldevelopment | Investigadores | |
| dcterms.audience.professionaldevelopment | Estudiantes | |
| oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |