Análisis de causalidad para series de tiempo multivariadas funcionales

ilustraciones, diagramas

Autores:: Maya Orozco, Jhon Eduwin

Tipo de recurso:

Fecha de publicación:: 2022

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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dc.title.spa.fl_str_mv	Análisis de causalidad para series de tiempo multivariadas funcionales
dc.title.translated.eng.fl_str_mv	Causal analysis for multivariate functional time series
title	Análisis de causalidad para series de tiempo multivariadas funcionales
spellingShingle	Análisis de causalidad para series de tiempo multivariadas funcionales 510 - Matemáticas 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Series temporales Datos funcionales Causalidad de Granger Modelos Autorregresivos Funcionales (FAR) Modelos Autorregresivos Funcionales con variables exógenas (FARX) Time series Functional data Granger causality Functional Autorregresive Models (FAR) Functional Autorregresive Models with exogenous variables (FARX) data analysis time series análisis de datos serie temporal
title_short	Análisis de causalidad para series de tiempo multivariadas funcionales
title_full	Análisis de causalidad para series de tiempo multivariadas funcionales
title_fullStr	Análisis de causalidad para series de tiempo multivariadas funcionales
title_full_unstemmed	Análisis de causalidad para series de tiempo multivariadas funcionales
title_sort	Análisis de causalidad para series de tiempo multivariadas funcionales
dc.creator.fl_str_mv	Maya Orozco, Jhon Eduwin
dc.contributor.advisor.none.fl_str_mv	Calderón Villanueva, Sergio Alejandro Guevara González, Rubén Darío
dc.contributor.author.none.fl_str_mv	Maya Orozco, Jhon Eduwin
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
topic	510 - Matemáticas 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Series temporales Datos funcionales Causalidad de Granger Modelos Autorregresivos Funcionales (FAR) Modelos Autorregresivos Funcionales con variables exógenas (FARX) Time series Functional data Granger causality Functional Autorregresive Models (FAR) Functional Autorregresive Models with exogenous variables (FARX) data analysis time series análisis de datos serie temporal
dc.subject.proposal.spa.fl_str_mv	Series temporales Datos funcionales Causalidad de Granger Modelos Autorregresivos Funcionales (FAR) Modelos Autorregresivos Funcionales con variables exógenas (FARX)
dc.subject.proposal.eng.fl_str_mv	Time series Functional data Granger causality Functional Autorregresive Models (FAR) Functional Autorregresive Models with exogenous variables (FARX)
dc.subject.wikidata.spa.fl_str_mv	data analysis time series
dc.subject.wikidata.eng.fl_str_mv	análisis de datos serie temporal
description	ilustraciones, diagramas
publishDate	2022
dc.date.issued.none.fl_str_mv	2022
dc.date.accessioned.none.fl_str_mv	2023-08-08T17:00:18Z
dc.date.available.none.fl_str_mv	2023-08-08T17:00:18Z
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
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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	Bosq, D. (2000). Linear processes in function spaces: theory and applications (Vol. 149). Springer Science & Business Media Boudjellaba, H., Dufour, J.-M., & Roy, R. (1992). Testing causality between two vectors in multivariate autoregressive moving average models. Journal of the American Statis- tical Association, 87 (420), 1082-1090. Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting. Springer. Cabassi, A., & Kashlak, A. B. (2017). fdcov: Analysis of Covariance Operators [R package version 1.1.0]. https://CRAN.R-project.org/package=fdcov Chen, Y., Chua, W. S., & Härdle, W. K. (2019). Forecasting limit order book liquidity supply–demand curves with functional autoregressive dynamics. Quantitative Finan ce, 19 (9), 1473-1489 Chen, Y., Koch, T., Lim, K. G., Xu, X., & Zakiyeva, N. (2021). A review study of functional autoregressive models with application to energy forecasting. Wiley Interdisciplinary Reviews: Computational Statistics, 13 (3), e1525. Conway, J. B. (2019). A course in functional analysis (Vol. 96). Springer. Cuevas, A. (2014). A partial overview of the theory of statistics with functional data. Journal of Statistical Planning and Inference, 147, 1-23. Damon, J., & Guillas, S. (2005). Estimation and simulation of autoregressive hilbertian pro cesses with exogenous variables. Statistical Inference for Stochastic Processes, 8 (2), 185-204. Elmezouar, Z. C. (2020). Functional causality between oil prices and GDP Based on Big Data. Computers, Materials & Continua, 63 (2), 593-604. Ferraty, F., & Romain, Y. (2011). The Oxford handbook of functional data analaysis. Oxford University Press. Fremdt, S., Steinebach, J. G., Horváth, L., & Kokoszka, P. (2013). Testing the equality of covariance operators in functional samples. Scandinavian Journal of Statistics, 40 (1), 138-152. Granger, C. W. (1969). Investigating causal relations by econometric models and cross spectral methods. Econometrica: journal of the Econometric Society, 424-438. Hörmann, S., Kidziński, Ł., & Hallin, M. (2015). Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77 (2), 319-348. Hörmann, S., & Kokoszka, P. (2010). Weakly dependent functional data. The Annals of Statistics, 38 (3), 1845-1884. Horváth, L., & Kokoszka, P. (2012). Inference for functional data with applications (Vol. 200). Springer Science & Business Media. Julio-Román, J. M., & Gamboa-Estrada, F. (2019). The Exchange Rate and Oil Prices in Colombia: A High Frequency Analysis. Borradores de Economía; No. 1091. Julio-Román, J. M., Rincón-Torres, A. D., & Rojas-Silva, K. (2021). The Interdependence of FX and Treasury Bonds Markets: The Case of Colombia. Borradores de Economía; No. 1171. Kidzinski, L., Jouzdani, N., & Kokoszka, P. (2017). pcdpca: Dynamic Principal Components for Periodically Correlated Functional Time Series [R package version 0.4]. https: //CRAN.R-project.org/package=pcdpca Kokoszka, P., & Reimherr, M. (2017). Introduction to functional data analysis. Chapman; Hall/CRC. Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer Science & Business Media. Panaretos, V. M., Kraus, D., & Maddocks, J. H. (2010). Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles. Journal of the Ame rican Statistical Association, 105 (490), 670-682. https://doi.org/10.1198/jasa.2010.tm09239 Panaretos, V. M., & Tavakoli, S. (2013). Fourier analysis of stationary time series in function space. The Annals of Statistics, 41 (2), 568-603. Pfaff, B. (2008). VAR, SVAR and SVEC Models: Implementation Within R Package vars. Journal of Statistical Software, 27 (4). https://www.jstatsoft.org/v27/i04/ Pindyck, R. S., Rubinfeld, D. L., & Rabasco, E. (2013). Microeconomia. Pearson Educación. Ramsay, J. O., Graves, S., & Hooker, G. (2022). fda: Functional Data Analysis [R package version 6.0.5]. https://CRAN.R-project.org/package=fda Ramsay, J. O., & Silverman, B. W. (2005). Functional Data Analysis. Springer. https://doi. org/https://doi.org/10.1007/b98888 Ramsay, J. O., & Silverman, B. W. (2002). Applied functional data analysis: methods and case studies (Vol. 77). Springer. S., H., & L., K. (2022a). freqdom: Frequency Domain Based Analysis: Dynamic PCA [R package version 2.0.3]. https://CRAN.R-project.org/package=freqdom S., H., & L., K. (2022b). freqdom.fda: Functional Time Series: Dynamic Functional Principal Components [R package version 1.0.1]. https: / / CRAN. R - project. org / package = freqdom.fda Sancetta, A. (2019). Intraday end-of-day volume prediction. Journal of Financial Econometrics. Saumard, M. (2017). Linear causality in the sense of Granger with stationary functional time series. En Functional Statistics and Related Fields (pp. 225-231). Springer. Saumard, M., & Hadjadji, B. (2021). Dynamic Functional Principal Components for Testing Causality. Signals, 2 (2), 353-365. Sen, R., Majumdar, A., & Sikaria, S. (2022). Bayesian Testing Of Granger Causality In Functional Time Series. Journal of Quantitative Economics, 1-20. Serge, D. J. G. (2022). far: Modelization for Functional AutoRegressive Processes [R package version 0.6-6]. https://CRAN.R-project.org/package=far Seth, A. (2007). Granger causality. Scholarpedia, 2 (7), 1667. Shojaie, A., & Fox, E. B. (2022). Granger causality: A review and recent advances. Annual Review of Statistics and Its Application, 9, 289-319. Sims, C. A. (1972). Money, income, and causality. The American economic review, 62 (4), 540-552. Skoog, G. R., et al. (1976). Causality Characterizations: Bivariate, Trivariate, and Multivariate Propositions (inf. téc.). Federal Reserve Bank of Minneapolis. Sonmez, O., Aue, A., & Rice, G. (2019). fChange: Change Point Analysis in Functional Data [R package version 0.2.1]. https://CRAN.R-project.org/package=fChange Srivastava, A., & Klassen, E. P. (2016). Functional and shape data analysis (Vol. 1). Springer. Virta, J., Li, B., Nordhausen, K., & Oja, H. (2020). Independent component analysis for multivariate functional data. Journal of Multivariate Analysis, 176, 104568. Wiener, N. (1956). The theory of prediction. Modern mathematics for engineers. Williams, D., Goodhart, C. A., & Gowland, D. H. (1976). Money, income, and causality: The UK experience. The American Economic Review, 66 (3), 417-423. Zhang, J. (2014). Analysis of variance for functional data. Monographs on statistics and applied probability, 127, 127. Zhang, X., & Shao, X. (2015). Two sample inference for the second-order property of temporally dependent functional data. Bernoulli, 21 (2), 909-929
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dc.format.extent.spa.fl_str_mv	xvi, 103 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
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spelling	Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Calderón Villanueva, Sergio Alejandro4435821363acfcc5a0b97c50464db9d4Guevara González, Rubén Darío1576c12a39d4ac35f1f710837eff755bMaya Orozco, Jhon Eduwinfa0e65bca46f6936bbbca53a876c4b402023-08-08T17:00:18Z2023-08-08T17:00:18Z2022https://repositorio.unal.edu.co/handle/unal/84489Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasLa causalidad de Granger es una prueba creada hace casi medio siglo que permite saber si una serie temporal ayuda en la predicción de otra. Para el caso de series temporales fun- cionales el tema ha sido explorado por autores como Saumard y Hadjadji (2021) o Sen et al. (2022), sin embargo el tema posee aún muchas lineas de investigación abiertas que han sido poco exploradas. Este trabajo se concentra en estudiar una extensión de las pruebas de causalidad de Granger para series de tiempo funcionales multivariadas de dimensiones mayores a 2 (específicamente 3 y 4), basada en los procedimientos propuestos por Saumard y Hadjadji (2021). Para este fin se simulan procesos bivariados, tri-variados y tetra-variados a partir de modelos FAR(1) y FARX(1). Se realizan las pruebas de causalidad de Granger a través de tres procedimientos (DFPCA, F-causalidad y G-causalidad). Se encuentra que la prueba que presenta mejores resultados a través del estudio de simulación es la que hace uso de los componentes principales dinámicos DFPCA y que la variabilidad explicada por el número de componentes afecta de manera sensible la potencia de la prueba. Se realiza un ejemplo de aplicación para ilustrar los procedimientos propuestos en el que se verifica si existe causalidad entre el precio del dólar (Yt), el precio del petróleo Brent (Xt1 ) y la tasa de interés de los bonos colombianos a 10 años (Xt2 ). Se confirma la causalidad de las variables Xti sobre la variable Yt tal y como la teoría económica parece predecir. (Texto tomado de la fuente)Granger causality is a test created almost half a century ago that allows us to know if one time series helps in the prediction of another. In the case of functional time series, the topic has been explored by authors such as Saumard y Hadjadji (2021) or Sen et al. (2022), however the topic still has many open lines of research that have been little explored. This work focuses on studying an extension of the Granger causality tests for multivariate functio- nal time series of dimensions greater than 2 (specifically 3 and 4), based on the procedures proposed by Saumard y Hadjadji (2021). For this purpose, bivariate, trivariate and tetra- variate processes are simulated using FAR(1) and FARX(1) models. Granger causality tests are carried out through three procedures (DFPCA, F-causality and G-causality). It is found that the test that presents the best results through the simulation study is the one that ma- kes use of the DFPCA dynamic principal components and that it will have been explained by the number of components that significantly affects the power of the test. An application example is carried out to illustrate the proposed procedures in which it is verified if there is causality between the price of the dollar (Yt), the price of Brent oil (Xt1 ) and the interest rate of the Colombian 10-year bonds (Xt2 ). The causality of the variables Xti on the variable Yt is confirmed, as economic theory seems to predict.MaestríaMagíster en Ciencias - EstadísticaSeries Temporales y Datos Funcionalesxvi, 103 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasSeries temporalesDatos funcionalesCausalidad de GrangerModelos Autorregresivos Funcionales (FAR)Modelos Autorregresivos Funcionales con variables exógenas (FARX)Time seriesFunctional dataGranger causalityFunctional Autorregresive Models (FAR)Functional Autorregresive Models with exogenous variables (FARX)data analysistime seriesanálisis de datosserie temporalAnálisis de causalidad para series de tiempo multivariadas funcionalesCausal analysis for multivariate functional time seriesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBosq, D. (2000). Linear processes in function spaces: theory and applications (Vol. 149). Springer Science & Business MediaBoudjellaba, H., Dufour, J.-M., & Roy, R. (1992). Testing causality between two vectors in multivariate autoregressive moving average models. Journal of the American Statis- tical Association, 87 (420), 1082-1090.Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting. Springer.Cabassi, A., & Kashlak, A. B. (2017). fdcov: Analysis of Covariance Operators [R package version 1.1.0]. https://CRAN.R-project.org/package=fdcovChen, Y., Chua, W. S., & Härdle, W. K. (2019). Forecasting limit order book liquidity supply–demand curves with functional autoregressive dynamics. Quantitative Finan ce, 19 (9), 1473-1489Chen, Y., Koch, T., Lim, K. G., Xu, X., & Zakiyeva, N. (2021). A review study of functional autoregressive models with application to energy forecasting. Wiley Interdisciplinary Reviews: Computational Statistics, 13 (3), e1525.Conway, J. B. (2019). A course in functional analysis (Vol. 96). Springer.Cuevas, A. (2014). A partial overview of the theory of statistics with functional data. Journal of Statistical Planning and Inference, 147, 1-23.Damon, J., & Guillas, S. (2005). Estimation and simulation of autoregressive hilbertian pro cesses with exogenous variables. Statistical Inference for Stochastic Processes, 8 (2), 185-204.Elmezouar, Z. C. (2020). Functional causality between oil prices and GDP Based on Big Data. Computers, Materials & Continua, 63 (2), 593-604.Ferraty, F., & Romain, Y. (2011). The Oxford handbook of functional data analaysis. Oxford University Press.Fremdt, S., Steinebach, J. G., Horváth, L., & Kokoszka, P. (2013). Testing the equality of covariance operators in functional samples. Scandinavian Journal of Statistics, 40 (1), 138-152.Granger, C. W. (1969). Investigating causal relations by econometric models and cross spectral methods. Econometrica: journal of the Econometric Society, 424-438.Hörmann, S., Kidziński, Ł., & Hallin, M. (2015). Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77 (2), 319-348.Hörmann, S., & Kokoszka, P. (2010). Weakly dependent functional data. The Annals of Statistics, 38 (3), 1845-1884.Horváth, L., & Kokoszka, P. (2012). Inference for functional data with applications (Vol. 200). Springer Science & Business Media.Julio-Román, J. M., & Gamboa-Estrada, F. (2019). The Exchange Rate and Oil Prices in Colombia: A High Frequency Analysis. Borradores de Economía; No. 1091.Julio-Román, J. M., Rincón-Torres, A. D., & Rojas-Silva, K. (2021). The Interdependence of FX and Treasury Bonds Markets: The Case of Colombia. Borradores de Economía; No. 1171.Kidzinski, L., Jouzdani, N., & Kokoszka, P. (2017). pcdpca: Dynamic Principal Components for Periodically Correlated Functional Time Series [R package version 0.4]. https: //CRAN.R-project.org/package=pcdpcaKokoszka, P., & Reimherr, M. (2017). Introduction to functional data analysis. Chapman; Hall/CRC.Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer Science & Business Media.Panaretos, V. M., Kraus, D., & Maddocks, J. H. (2010). Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles. Journal of the Ame rican Statistical Association, 105 (490), 670-682. https://doi.org/10.1198/jasa.2010.tm09239Panaretos, V. M., & Tavakoli, S. (2013). Fourier analysis of stationary time series in function space. The Annals of Statistics, 41 (2), 568-603.Pfaff, B. (2008). VAR, SVAR and SVEC Models: Implementation Within R Package vars. Journal of Statistical Software, 27 (4). https://www.jstatsoft.org/v27/i04/Pindyck, R. S., Rubinfeld, D. L., & Rabasco, E. (2013). Microeconomia. Pearson Educación.Ramsay, J. O., Graves, S., & Hooker, G. (2022). fda: Functional Data Analysis [R package version 6.0.5]. https://CRAN.R-project.org/package=fdaRamsay, J. O., & Silverman, B. W. (2005). Functional Data Analysis. Springer. https://doi. org/https://doi.org/10.1007/b98888Ramsay, J. O., & Silverman, B. W. (2002). Applied functional data analysis: methods and case studies (Vol. 77). Springer.S., H., & L., K. (2022a). freqdom: Frequency Domain Based Analysis: Dynamic PCA [R package version 2.0.3]. https://CRAN.R-project.org/package=freqdomS., H., & L., K. (2022b). freqdom.fda: Functional Time Series: Dynamic Functional Principal Components [R package version 1.0.1]. https: / / CRAN. R - project. org / package = freqdom.fdaSancetta, A. (2019). Intraday end-of-day volume prediction. Journal of Financial Econometrics.Saumard, M. (2017). Linear causality in the sense of Granger with stationary functional time series. En Functional Statistics and Related Fields (pp. 225-231). Springer.Saumard, M., & Hadjadji, B. (2021). Dynamic Functional Principal Components for Testing Causality. Signals, 2 (2), 353-365.Sen, R., Majumdar, A., & Sikaria, S. (2022). Bayesian Testing Of Granger Causality In Functional Time Series. Journal of Quantitative Economics, 1-20.Serge, D. J. G. (2022). far: Modelization for Functional AutoRegressive Processes [R package version 0.6-6]. https://CRAN.R-project.org/package=farSeth, A. (2007). Granger causality. Scholarpedia, 2 (7), 1667.Shojaie, A., & Fox, E. B. (2022). Granger causality: A review and recent advances. Annual Review of Statistics and Its Application, 9, 289-319.Sims, C. A. (1972). Money, income, and causality. The American economic review, 62 (4), 540-552.Skoog, G. R., et al. (1976). Causality Characterizations: Bivariate, Trivariate, and Multivariate Propositions (inf. téc.). Federal Reserve Bank of Minneapolis.Sonmez, O., Aue, A., & Rice, G. (2019). fChange: Change Point Analysis in Functional Data [R package version 0.2.1]. https://CRAN.R-project.org/package=fChangeSrivastava, A., & Klassen, E. P. (2016). Functional and shape data analysis (Vol. 1). Springer.Virta, J., Li, B., Nordhausen, K., & Oja, H. (2020). Independent component analysis for multivariate functional data. Journal of Multivariate Analysis, 176, 104568.Wiener, N. (1956). The theory of prediction. Modern mathematics for engineers.Williams, D., Goodhart, C. A., & Gowland, D. H. (1976). Money, income, and causality: The UK experience. The American Economic Review, 66 (3), 417-423.Zhang, J. (2014). Analysis of variance for functional data. Monographs on statistics and applied probability, 127, 127.Zhang, X., & Shao, X. (2015). Two sample inference for the second-order property of temporally dependent functional data. Bernoulli, 21 (2), 909-929EstudiantesInvestigadoresPadres y familiasPúblico generalORIGINAL1094949022.2023.pdf1094949022.2023.pdfTesis de Maestría en Ciencias - Estadísticaapplication/pdf2229268https://repositorio.unal.edu.co/bitstream/unal/84489/2/1094949022.2023.pdf9f83e357b26e6c4096c61f879d52c400MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84489/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51THUMBNAIL1094949022.2023.pdf.jpg1094949022.2023.pdf.jpgGenerated Thumbnailimage/jpeg4126https://repositorio.unal.edu.co/bitstream/unal/84489/3/1094949022.2023.pdf.jpg18d8a9a7815fadaa5608c562c2e4c229MD53unal/84489oai:repositorio.unal.edu.co:unal/844892023-08-08 23:03:25.009Repositorio Institucional Universidad Nacional de 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