Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano

ilustraciones, graficas

Autores:: Rivera Garzón, Nicolás

Tipo de recurso:

Fecha de publicación:: 2023

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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dc.title.spa.fl_str_mv	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano
dc.title.translated.eng.fl_str_mv	Forecasts based on a multivariate autoregressive threshold model (MTAR) with a multivariate t-Student error distribution from a Bayesian approach
title	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano
spellingShingle	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas TEORIA BAYESIANA DE DECISIONES ESTADISTICAS CONSTRUCCION DE MODELOS Bayesian statistical decision theory Models and modelmaking Modelos MTAR Estadística Bayesiana Pronósticos Distribución predictiva Distribución t-Student Modelos no lineales MTAR models Bayesian statistics Forecasting Predictive distribution Student's t-distribution Nonlinear models
title_short	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano
title_full	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano
title_fullStr	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano
title_full_unstemmed	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano
title_sort	Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano
dc.creator.fl_str_mv	Rivera Garzón, Nicolás
dc.contributor.advisor.none.fl_str_mv	Calderón Villanueva, Sergio Alejandro Espinosa Acuña, Oscar Andrés
dc.contributor.author.none.fl_str_mv	Rivera Garzón, Nicolás
dc.contributor.researchgroup.spa.fl_str_mv	Grupo de Investigación en Modelos Económicos y Métodos Cuantitativos (Imemc)
dc.contributor.orcid.spa.fl_str_mv	0000-0002-0044-5435
dc.contributor.googlescholar.spa.fl_str_mv	BRJcH4UAAAAJ
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
topic	510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas TEORIA BAYESIANA DE DECISIONES ESTADISTICAS CONSTRUCCION DE MODELOS Bayesian statistical decision theory Models and modelmaking Modelos MTAR Estadística Bayesiana Pronósticos Distribución predictiva Distribución t-Student Modelos no lineales MTAR models Bayesian statistics Forecasting Predictive distribution Student's t-distribution Nonlinear models
dc.subject.lemb.spa.fl_str_mv	TEORIA BAYESIANA DE DECISIONES ESTADISTICAS CONSTRUCCION DE MODELOS
dc.subject.lemb.eng.fl_str_mv	Bayesian statistical decision theory Models and modelmaking
dc.subject.proposal.spa.fl_str_mv	Modelos MTAR Estadística Bayesiana Pronósticos Distribución predictiva Distribución t-Student Modelos no lineales
dc.subject.proposal.eng.fl_str_mv	MTAR models Bayesian statistics Forecasting Predictive distribution Student's t-distribution Nonlinear models
description	ilustraciones, graficas
publishDate	2023
dc.date.accessioned.none.fl_str_mv	2023-05-31T16:27:30Z
dc.date.available.none.fl_str_mv	2023-05-31T16:27:30Z
dc.date.issued.none.fl_str_mv	2023
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
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dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/83929
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/83929 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	spa
language	spa
dc.relation.references.spa.fl_str_mv	Anthony, M., y Harvey, M. (2012). Linear algebra: concepts and methods. Cambridge University Press. Barnard, J., McCulloch, R., y Meng, X. (2000). Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statistica Sinica, 10 (4), 1281-1311. Bartkowiak, A. (2007). Should normal distribution be normal? The student's t alternative. En 6th international conference on computer information systems and industrial management applications (cisim'07) (p. 3-8). Bickel, P., y Doksum, K. (2015). Basic ideas and selected topics, volumes i-ii (2nd ed.). Chapman and Hall/CRC. Calderón, S., y Nieto, F. (2017). Bayesian analysis of multivariate threshold autoregressive models with missing data. Communications in Statistics - Theory and Methods, 46 (1), 296-318. Calderón, S., y Nieto, F. (2021). Forecasting with multivariate threshold autoregressive models. Revista Colombiana de Estadística, 44 (2), 369-383. Chen, C., y Lee, J. (1995). Bayesian inference of threshold autoregressive. Journal of Time Series Analysis, 16 (5), 483-492. Chiu, C., Mumtaz, H., y Pint er, G. (2017). Forecasting with VAR models: Fat tails and stochastic volatility. International Journal of Forecasting, 33 (4), 1124-1143. Debski, W. (2010). Chapter 1: Probabilistic inverse theory. En R. Dmowska (Ed.), Advances in geophysics (Vol. 52, p. 1-102). Elsevier. Diebold, F., y Mariano, R. (1995). Comparing predictive accuracy. Journal of Business Economic Statistics, 13 (3), 253-63. Espinosa, O., y Nieto, F. (2016). Estudio del efecto de apalancamiento en series financieras usando un modelo TAR. Universidad Nacional de Colombia, Bogotá, D.C . Gelman, A., Carlin, J., Stern, H., y Rubin, D. (2004). Bayesian data analysis (2nd ed.). Chapman and Hall/CRC. Gelman, A., y Rubin, D. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7 (4), 457 - 472. Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In bayesian statistics (pp. 169-193). González, J., y Nieto, F. (2020). Bayesian analysis of multiplicative seasonal threshold autoregressive processes. Revista Colombiana de Estadística, 43 (2), 251-284. Hansen, B. (1997). Inference in TAR models. Studies in nonlinear dynamics and econometrics, 2 , 1-14. Hansen, B. (1999). Testing for linearity. Journal of Economic Surveys, 13 (5), 551-576. Hansen, B. (2011). Threshold autoregression in economics. Statistics and Its Interface Volume, 4 , 123-127. Harvey, D., Leybourne, S., y Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13 (2), 281-291. Hyndman, R., y Athanasopoulos, G. (2018). Forecasting: principles and practice (2nd ed.). Australia: OTexts. Ibáñez, L., y Calderón, S. (2020). Estimación bayesiana de los parámetros estructurales de los modelos multivariados autoregresivos de umbrales con ruido t-student multivariado. Universidad Nacional de Colombia, Bogotá, D.C . Karlsson, S. (2013). Forecasting with bayesian vector autoregression. En G. Elliott y A. Timmermann (Eds.), Handbook of economic forecasting (Vol. 2, p. 791-897). Elsevier. Kibria, G., y Joarder, A. (2006). A short review of multivariate t-distribution. Journal of Statistical Research ISSN , 40 , 256-422. Li, D., y Tong, H. (2016). Nested sub-sample search algorithm for estimation of threshold models. Statistica Sinica, 26 (4), 1543-1554. Lo, M., y Zivot, E. (2001). Threshold cointegration and nonlinear adjustment to the law of one price. Macroeconomic Dynamics, 5 (4), 533-576. Nieto, F. (2005). Modeling bivariate threshold autoregressive processes in the presence of missing data. Communications in Statistics - Theory and Methods, 34 (4), 905-930. Nieto, F. (2008). Forecasting with univariate TAR models. Statistical Methodology, 5 (3), 263-276. Nieto, F., Zhang, H., y Li, W. (2013). Using the reversible jump MCMC procedure for identifying and estimating univariate TAR models. Communications in Statistics - Simulation and Computation, 42 (4), 814-840. Romero, L., y Calderón, S. (2021). Bayesian estimation of a multivariate tar model when the noise process follows a student-t distribution. Communications in Statistics - Theory and Methods, 50 (11), 2508-2530. Tong, H. (1978). On a threshold model. In: C. Chen (Ed.), Pattern recognition and signal processing. Amsterdam: Sijhoff Noordhoff., 42 , 575-586. Tong, H. (1990). Non-linear time series: a dynamical system approach. Oxford: Oxford Statistical Science, Oxford University Press. Tong, H. (2015). Threshold models in time series analysis - some reflections. Journal of Econometrics, 189 (2), 485-491. Tong, H., y Lim, K. (1980). Threshold autoregression, limit cycles. Journal of the Royal Statistical Society: Series B (Methodological), 42 (3), 245-268. Tsay, R. (1998). Testing and modeling multivariate threshold models. Journal of the American Statistical Association, 93 (443), 1188-1202. Tsay, R., y Chen, R. (2019). Nonlinear time series analysis. John Wiley Sons, Inc. Vaca, P., y Nieto, F. (2018). Analysis of the forecasting performance of the threshold autoregressive model. Universidad Nacional de Colombia, Bogotá, D.C . Wong, S., Chan, W., y Kam, P. (2009). A Student t-mixture autoregressive model with applications to heavy-tailed financial data. Biometrika, 96 (3), 751-760. Zhang, H., y Nieto, F. (2015). TAR modeling with missing data when the white noise process follows a student's t-distribution. Revista Colombiana de Estadística, 38 (1), 239-265. Zivot, E., y Wang, J. (2005). Modeling nancial time series with S-Plus. Nieto, F., y Hoyos, M. (2011). Testing linearity against a univariate TAR speci fication in time series with missing data. Revista Colombiana de Estadística, 34 (1), 73-94.
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv	Atribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rights.uri.spa.fl_str_mv	http://creativecommons.org/licenses/by-nc-nd/4.0/
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rights_invalid_str_mv	Atribución-NoComercial-SinDerivadas 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ http://purl.org/coar/access_right/c_abf2
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dc.format.extent.spa.fl_str_mv	xvi, 82 páginas
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Maestría en Ciencias - Estadística
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Calderón Villanueva, Sergio Alejandro4435821363acfcc5a0b97c50464db9d4Espinosa Acuña, Oscar Andrés268b9e01a0ae0fcbf5a44a4baa532318Rivera Garzón, Nicolás6227bfde3b1a9d044753b00ed0ff9b62Grupo de Investigación en Modelos Económicos y Métodos Cuantitativos (Imemc)0000-0002-0044-5435BRJcH4UAAAAJ2023-05-31T16:27:30Z2023-05-31T16:27:30Z2023https://repositorio.unal.edu.co/handle/unal/83929Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, graficasEn este trabajo se presenta un método que permite obtener los pronósticos basados en un modelo MTAR con distribución de error t-Student multivariada desde el enfoque Bayesiano. Para ello, se encuentra la distribución predictiva Bayesiana que incluye la incertidumbre sobre los verdaderos valores de los parámetros del modelo MTAR. El procedimiento planteado se basa en la obtención de muestras de la distribución predictiva para obtener el pronóstico puntual e intervalos de predicción del proceso de interés. El desempeño del algoritmo planteado se verifica a través de un estudio de simulación basado en tres modelos en donde se calcula el porcentaje de veces en que los valores verdaderos del proceso de salida se encuentran dentro del intervalo de predicción del 95% de la distribución predictiva. Posteriormente se presenta una aplicación a un conjunto de series de tiempo financieras donde se obtienen los pronósticos de los retornos de los índices Bovespa y Colcap usando como variable umbral los retornos del índice Standard and Poor's 500 y se comparan los pronósticos con los obtenidos por un modelo MTAR con distribución de error normal multivariada. (Texto tomado de la fuente)This paper presents a Bayesian method to obtain forecasts based on a MTAR model with a multivariate t-Student error distribution. For this, the Bayesian predictive distribution is found, which includes the uncertainty about the true values of the parameters of the MTAR model. The proposed procedure is based on drawing samples from the predictive distribution to obtain the point forecast and prediction intervals of the process of interest. The performance of the proposed algorithm is veri fied through a simulation study based on three models where the percentage of times in which the true values of the output process are within the prediction interval of 95% of the predictive distribution is calculated. Subsequently, an application to a set of financial time series is presented where the forecasts of the returns of the Bovespa and Colcap indexes are obtained using the returns of the Standard and Poor's 500 index as a threshold variable and the forecasts are compared with those obtained by a MTAR model with multivariate normal error distribution.MaestríaMagíster en Ciencias - EstadísticaSeries de Tiempoxvi, 82 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasTEORIA BAYESIANA DE DECISIONES ESTADISTICASCONSTRUCCION DE MODELOSBayesian statistical decision theoryModels and modelmakingModelos MTAREstadística BayesianaPronósticosDistribución predictivaDistribución t-StudentModelos no linealesMTAR modelsBayesian statisticsForecastingPredictive distributionStudent's t-distributionNonlinear modelsPronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque BayesianoForecasts based on a multivariate autoregressive threshold model (MTAR) with a multivariate t-Student error distribution from a Bayesian approachTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAnthony, M., y Harvey, M. (2012). Linear algebra: concepts and methods. Cambridge University Press.Barnard, J., McCulloch, R., y Meng, X. (2000). Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statistica Sinica, 10 (4), 1281-1311.Bartkowiak, A. (2007). Should normal distribution be normal? The student's t alternative. En 6th international conference on computer information systems and industrial management applications (cisim'07) (p. 3-8).Bickel, P., y Doksum, K. (2015). Basic ideas and selected topics, volumes i-ii (2nd ed.). Chapman and Hall/CRC.Calderón, S., y Nieto, F. (2017). Bayesian analysis of multivariate threshold autoregressive models with missing data. Communications in Statistics - Theory and Methods, 46 (1), 296-318.Calderón, S., y Nieto, F. (2021). Forecasting with multivariate threshold autoregressive models. Revista Colombiana de Estadística, 44 (2), 369-383.Chen, C., y Lee, J. (1995). Bayesian inference of threshold autoregressive. Journal of Time Series Analysis, 16 (5), 483-492.Chiu, C., Mumtaz, H., y Pint er, G. (2017). Forecasting with VAR models: Fat tails and stochastic volatility. International Journal of Forecasting, 33 (4), 1124-1143.Debski, W. (2010). Chapter 1: Probabilistic inverse theory. En R. Dmowska (Ed.), Advances in geophysics (Vol. 52, p. 1-102). Elsevier.Diebold, F., y Mariano, R. (1995). Comparing predictive accuracy. Journal of Business Economic Statistics, 13 (3), 253-63.Espinosa, O., y Nieto, F. (2016). Estudio del efecto de apalancamiento en series financieras usando un modelo TAR. Universidad Nacional de Colombia, Bogotá, D.C .Gelman, A., Carlin, J., Stern, H., y Rubin, D. (2004). Bayesian data analysis (2nd ed.). Chapman and Hall/CRC.Gelman, A., y Rubin, D. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7 (4), 457 - 472.Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In bayesian statistics (pp. 169-193).González, J., y Nieto, F. (2020). Bayesian analysis of multiplicative seasonal threshold autoregressive processes. Revista Colombiana de Estadística, 43 (2), 251-284.Hansen, B. (1997). Inference in TAR models. Studies in nonlinear dynamics and econometrics, 2 , 1-14.Hansen, B. (1999). Testing for linearity. Journal of Economic Surveys, 13 (5), 551-576.Hansen, B. (2011). Threshold autoregression in economics. Statistics and Its Interface Volume, 4 , 123-127.Harvey, D., Leybourne, S., y Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13 (2), 281-291.Hyndman, R., y Athanasopoulos, G. (2018). Forecasting: principles and practice (2nd ed.). Australia: OTexts.Ibáñez, L., y Calderón, S. (2020). Estimación bayesiana de los parámetros estructurales de los modelos multivariados autoregresivos de umbrales con ruido t-student multivariado. Universidad Nacional de Colombia, Bogotá, D.C .Karlsson, S. (2013). Forecasting with bayesian vector autoregression. En G. Elliott y A. Timmermann (Eds.), Handbook of economic forecasting (Vol. 2, p. 791-897). Elsevier.Kibria, G., y Joarder, A. (2006). A short review of multivariate t-distribution. Journal of Statistical Research ISSN , 40 , 256-422.Li, D., y Tong, H. (2016). Nested sub-sample search algorithm for estimation of threshold models. Statistica Sinica, 26 (4), 1543-1554.Lo, M., y Zivot, E. (2001). Threshold cointegration and nonlinear adjustment to the law of one price. Macroeconomic Dynamics, 5 (4), 533-576.Nieto, F. (2005). Modeling bivariate threshold autoregressive processes in the presence of missing data. Communications in Statistics - Theory and Methods, 34 (4), 905-930.Nieto, F. (2008). Forecasting with univariate TAR models. Statistical Methodology, 5 (3), 263-276.Nieto, F., Zhang, H., y Li, W. (2013). Using the reversible jump MCMC procedure for identifying and estimating univariate TAR models. Communications in Statistics - Simulation and Computation, 42 (4), 814-840.Romero, L., y Calderón, S. (2021). Bayesian estimation of a multivariate tar model when the noise process follows a student-t distribution. Communications in Statistics - Theory and Methods, 50 (11), 2508-2530.Tong, H. (1978). On a threshold model. In: C. Chen (Ed.), Pattern recognition and signal processing. Amsterdam: Sijhoff Noordhoff., 42 , 575-586.Tong, H. (1990). Non-linear time series: a dynamical system approach. Oxford: Oxford Statistical Science, Oxford University Press.Tong, H. (2015). Threshold models in time series analysis - some reflections. Journal of Econometrics, 189 (2), 485-491.Tong, H., y Lim, K. (1980). Threshold autoregression, limit cycles. Journal of the Royal Statistical Society: Series B (Methodological), 42 (3), 245-268.Tsay, R. (1998). Testing and modeling multivariate threshold models. Journal of the American Statistical Association, 93 (443), 1188-1202.Tsay, R., y Chen, R. (2019). Nonlinear time series analysis. John Wiley Sons, Inc.Vaca, P., y Nieto, F. (2018). Analysis of the forecasting performance of the threshold autoregressive model. Universidad Nacional de Colombia, Bogotá, D.C .Wong, S., Chan, W., y Kam, P. (2009). A Student t-mixture autoregressive model with applications to heavy-tailed financial data. Biometrika, 96 (3), 751-760.Zhang, H., y Nieto, F. (2015). TAR modeling with missing data when the white noise process follows a student's t-distribution. Revista Colombiana de Estadística, 38 (1), 239-265.Zivot, E., y Wang, J. (2005). Modeling nancial time series with S-Plus.Nieto, F., y Hoyos, M. (2011). Testing linearity against a univariate TAR speci fication in time series with missing data. Revista Colombiana de Estadística, 34 (1), 73-94.EstudiantesInvestigadoresPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/83929/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53ORIGINAL1014298439.2023.pdf1014298439.2023.pdfTesis de Maestría en Ciencias - Estadísticaapplication/pdf1672145https://repositorio.unal.edu.co/bitstream/unal/83929/4/1014298439.2023.pdfb0b897492cdddf03c4814392e414a1b9MD54THUMBNAIL1014298439.2023.pdf.jpg1014298439.2023.pdf.jpgGenerated Thumbnailimage/jpeg5040https://repositorio.unal.edu.co/bitstream/unal/83929/5/1014298439.2023.pdf.jpgb79c28caa381a01f90d585c72c42383dMD55unal/83929oai:repositorio.unal.edu.co:unal/839292024-08-08 23:11:41.341Repositorio Institucional Universidad Nacional de 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Pronósticos basados en un modelo multivariado autorregresivo de umbrales (MTAR) con distribución de error t-Student multivariada desde el enfoque Bayesiano

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