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dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.contributor.advisorCepeda Cuervo, Edilberto
dc.contributor.authorCastaño Tafur, Yeferson Andrés
dc.identifier.citationCastaño Tafur, Y. (2020). Modelos lineales con cambio estructural: una perspectiva Bayesiana. Tesis de Maestría Universidad Nacional de Colombia.
dc.description.abstractIn this thesis, a Bayesian proposal for the estimation of normal linear regression models and longitudinal models both with structural change is presented. First, the proposal for estimating linear regression models with a change-point is introduced. Afterwards, this concept is gradually extended to regression models with heterocystic variance and structural change. Subsequently, the proposal for longitudinal models with a change-point and parametric covariance structures SC, AR(1) and ARMA(1,1) is being presented. The Bayesian methodology is implemented through the use of MCMC stochastic simulations across the Metropolis-Hastings within Gibbs algorithm. Additionally, the estimation of the change-point is made by a search on all possible values, this is optimized by the Transition Kernel proposed. Then, the performance of the algorithms is analyzed through simulation studies which allows concluding that the change-point is detected with great precision. Finally, the proposed models are applied on real data suggested in the literature and those are compared with models without structural change; it is found that the proposed models fit the data better. Thus, it is necessary to use the AIC and BIC goodness of fit statistics and the residual analysis.
dc.description.abstractEn esta tesis, se presenta una propuesta Bayesiana para la estimación de modelos de regresión lineal normal y modelos longitudinales con cambio estructural. Primero, se introduce la propuesta de estimación de modelos de regresión lineal con un punto de cambio. Luego, se amplía gradualmente este concepto a modelos de regresión con varianza heterocedástica y cambio estructural. Posteriormente, se presenta la propuesta para modelos longitudinales con un punto de cambio y estructuras paramétricas de covarianza SC, AR(1) y ARMA(1,1). La metodología Bayesiana se implementa mediante el uso de simulaciones estocásticas MCMC a través del algoritmo Metropolis-Hastings within Gibbs. Por otro lado, la estimación del punto de cambio se realiza con una búsqueda sobre todos los posibles valores, esta es optimizada por los núcleos de transición propuestos. Después, el rendimiento de los algoritmos es investigado mediante estudios de simulación y se concluye que se detecta el punto de cambio con una gran precisión. Finalmente, los modelos propuestos se aplican sobre datos reales sugeridos en la literatura y se comparan con modelos sin cambio estructural; se encuentra que los modelos propuestos ajustan mejor los datos, para esto se utilizan los estadísticos de bondad de ajuste AIC y BIC, y el análisis de residuales.
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.subject.ddc310 - Colecciones de estadística general
dc.subject.ddc519 - Probabilidades y matemáticas aplicadas
dc.subject.ddc658 - Gerencia general
dc.subject.ddc510 - Matemáticas
dc.titleModelos lineales con cambio estructural: una perspectiva Bayesiana
dc.title.alternativeLinear models with structural change: a Bayesian perspective
dc.rights.spaAcceso abierto
dc.publisher.programBogotá - Ciencias - Maestría en Ciencias - Estadística
dc.contributor.corporatenameUniversidad Nacional de Colombia - Sede Bogotá
dc.publisher.departmentDepartamento de Estadística
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotá
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dc.subject.proposalstructural change
dc.subject.proposalcambio estructural
dc.subject.proposalpunto de cambio
dc.subject.proposaldatos longitudinales
dc.subject.proposallongitudinal data
dc.subject.proposalcovariance structure
dc.subject.proposalestructura de covarianza

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Atribución-NoComercial-SinDerivadas 4.0 InternacionalThis work is licensed under a Creative Commons Reconocimiento-NoComercial 4.0.This document has been deposited by the author (s) under the following certificate of deposit