Análisis de factores comunes dinámicos en presencia de procesos de ruido autocorrelacionados
| dc.contributor.advisor | Nieto Sánchez, Fabio Humberto | spa |
| dc.contributor.advisor | Peña Sánchez de Rivera, Daniel | spa |
| dc.contributor.author | Bolívar Atuesta, Stevenson | spa |
| dc.contributor.researchgroup | Series de Tiempo | spa |
| dc.date.accessioned | 2021-01-27T22:38:47Z | spa |
| dc.date.available | 2021-01-27T22:38:47Z | spa |
| dc.date.issued | 2020-07-25 | spa |
| dc.description.abstract | This thesis presents a procedure to build a dynamic factor model in the presence of orthogonal stationary noise-processes. The procedure is based on the Peña-Box model (Peña & Box, 1987), in which the number of observed time series is fixed, and in the extension proposed by Peña & Poncela (2006) to non-stationary common factors, in which the common factors may be integrated processes. As a first result, an alternative for detecting the number of common factors is proposed by extending the statistical test of Peña & Poncela (2006), proposed for the Peña-Box model with a white noise process. Furthermore, in the same context, a statistical test is proposed to identify the number of non-stationary common factors. These proposals are illustrated by simulation and an application with real data, in which some empirical findings related to seasonal factors are also presented. The model is estimated by maximum likelihood, via a state-space model. | spa |
| dc.description.abstract | Esta tesis presenta un procedimiento para construir un modelo de factores comunes dinámicos en presencia de procesos de ruido estacionarios ortogonales. El procedimiento se basa en el modelo de Peña-Box (Peña & Box, 1987), en el cual el número de series de tiempo observadas es fijo, y en la extensión propuesta por Peña & Poncela (2006) a factores comunes no estacionarios, en la cual los factores comunes pueden ser procesos integrados. Como primer resultado, se propone una alternativa para la identificación del número de factores comunes extendiendo la prueba estadística de Peña & Poncela (2006) , propuesta para el modelo Peña-Box con proceso de ruido blanco. Adicionalmente, bajo el mismo contexto, se propone una prueba estadística para identificar el número de factores comunes no estacionarios. Estas propuestas son ilustradas mediante simulación y una aplicación con datos reales, en la cual también se presentan algunos hallazgos empíricos relacionados a factores estacionales. La estimación del modelo se realiza por máxima verosimilitud, vía un modelo espacio de estados. | spa |
| dc.description.additional | Línea de investigación: Series de Tiempo | spa |
| dc.description.degreelevel | Doctorado | spa |
| dc.format.extent | 97 | spa |
| dc.format.mimetype | application/pdf | spa |
| dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/78960 | |
| dc.language.iso | spa | spa |
| dc.publisher.branch | Universidad Nacional de Colombia - Sede Bogotá | spa |
| dc.publisher.department | Departamento de Estadística | spa |
| dc.publisher.program | Bogotá - Ciencias - Doctorado en Ciencias - Estadística | spa |
| dc.relation.references | Ahn, S. C. & Horenstein, A. R. (2013). Eigenvalue Ratio Test for the Number of Factors, Econometrica 81(3): 1203–1227. | spa |
| dc.relation.references | Alonso, A. M., Galeano, P. & Pe˜na, D. (2020). A robust procedure to build dynamic factor models with cluster structure, Journal of Econometrics. | spa |
| dc.relation.references | Amengual, D. & Watson, M. W. (2007). Consistent estimation of the number of dynamic factors in a large n and t panel, Journal of Business & Economic Statistics 25(1): 91– 96. | spa |
| dc.relation.references | Anderson, T. W. (1963b). The use of factor analysis in the statistical analysis of multiple time series, Psychometrika 28(1-25). | spa |
| dc.relation.references | Argyros, I. K. & d Hilout, S. (2013). Computational methods in nonlinear analysis: efficient algorithms, fixed point theory and applications, World Scientific. | spa |
| dc.relation.references | Bai, J. (2003). Inferential theory for factor models of large dimensions, Econometrica 71(1): 135–171. | spa |
| dc.relation.references | Bai, J. & Ng, S. (2002). Determining the number of factors in approximate factor models, Econometrica 70(191-222). | spa |
| dc.relation.references | Bai, J. & Ng, S. (2004). A panic attack on unit roots and cointegration., Econometrica 72(1127-1177). | spa |
| dc.relation.references | Bai, J. & Ng, S. (2007). Determining the number of primitive shocks in factor models, Journal of Business & Economic Statistics 25(1): 52–60. | spa |
| dc.relation.references | Bai, J. & Ng, S. (2010). Panel unit root tests with cross-section dependence: a further investigation, Econometric Theory 26(4): 1088–1114. | spa |
| dc.relation.references | Bai, J. & Wang, P. (2015). Identification and bayesian estimation of dynamic factor models, Journal of Business & Economic Statistics 33(2): 221–240. | spa |
| dc.relation.references | Bai, J. & Wang, P. (2016). Econometric analysis of large factor models, Annual Review of Economics 8(1): 53–80. | spa |
| dc.relation.references | Bickel, P. J., Levina, E. et al. (2008a). Covariance regularization by thresholding, The Annals of Statistics 36(6): 2577–2604. | spa |
| dc.relation.references | Bickel, P. J., Levina, E. et al. (2008b). Regularized estimation of large covariance matrices, The Annals of Statistics 36(1): 199–227. | spa |
| dc.relation.references | Bolívar, S., Nieto, F. H. & Peña, D. (2021). On a new procedure for identifying a dynamic common factor model, Revista Colombiana de Estadística 44(1): 1–21. | spa |
| dc.relation.references | Breitung, J. & Pigorsch, U. (2013). A canonical correlation approach for selecting the number of dynamic factors., Oxford Bulletin of Economics and Statistics 75(1): 23–36. | spa |
| dc.relation.references | Breitung, J. & Tenhofen, J. (2011). GLS estimation of dnamic factor models, Journal of the American Statistical Association 106(1150-1166). | spa |
| dc.relation.references | Cai, T. T., Ren, Z., Zhou, H. H. et al. (2016). Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation, Electronic Journal of Statistics 10(1): 1–59. | spa |
| dc.relation.references | Cai, T. T., Zhang, C.-H., Zhou, H. H. et al. (2010). Optimal rates of convergence for covariance matrix estimation, The Annals of Statistics 38(4): 2118–2144. | spa |
| dc.relation.references | Cai, T. T., Zhou, H. H. et al. (2012). Optimal rates of convergence for sparse covariance matrix estimation, The Annals of Statistics 40(5): 2389–2420. | spa |
| dc.relation.references | Chamberlain, G. (1983). Funds, factors, and diversification in arbitrage pricing models, Econometrica 51(5): 1305–1323. | spa |
| dc.relation.references | Chamberlain, G. & Rothschild, M. (1983). Arbitrage, factor structure, and mean-variance analysis on large asset markets, Econometrica 51(5): 1281–1304. | spa |
| dc.relation.references | Chudik, A., Pesaran, M. H. &Tosetti, E. (2011). Weak and strong cross-section dependence and estimation of large panels, The Econometrics Journal 14(1): C45–C90. | spa |
| dc.relation.references | Corona, F., Poncela, P. & Ruiz, E. (2017). Determining the number of factors after stationary univariate transformations, Empirical Economics 53(1): 351–372. | spa |
| dc.relation.references | Corona, F., Poncela, P. & Ruiz, E. (2020). Estimating non-stationary common factors: implications for risk sharing, Computational Economics 55(1): 37–60. | spa |
| dc.relation.references | Correal, M. E. (2007). Modelo Factorial Dinámico TAR, PhD thesis, Universidad Nacional de Colombia - Sede Bogotá. | spa |
| dc.relation.references | Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm, Journal of the Royal Statistical Society: Series B (Methodological) 39(1): 1–22. | spa |
| dc.relation.references | Doz, C. & Fuleky, P. (2019). Dynamic Factor Models. working paper or preprint. URL: https://halshs.archives-ouvertes.fr/halshs-02262202 | spa |
| dc.relation.references | Doz, C., Giannone, D. & Reichlin, L. (2011). A two-step estimator for large approximate dynamic factor models based on Kalman filtering, Journal of Econometrics 164(1): 188 – 205. | spa |
| dc.relation.references | Doz, C., Giannone, D. & Reichlin, L. (2012). A quasi-maximum likelihood approach for large, approximate dynamic factor models., Review of Economics and Statistics 94(4): 1014 – 1024. | spa |
| dc.relation.references | Fan, J., Fan, Y. & Lv, J. (2008). High dimensional covariance matrix estimation using a factor model, Journal of Econometrics 147(1): 186–197. | spa |
| dc.relation.references | Forni, M., Hallin, M., Lippi, M. & Reichlin, L. (2000). The generalized dynamic-factor model: Identification and estimation., Review ofEconomics and Statistics 82(4): 540– 554. | spa |
| dc.relation.references | Furrer, R. & Bengtsson, T. (2007). Estimation of high-dimensional prior and posterior covariance matrices in kalman filter variants, Journal of Multivariate Analysis 98(2): 227–255. | spa |
| dc.relation.references | Gayles, J. & Molenaar, P. (2013). The utility of person-specific analyses for investigating developmental processes: An analytic primer on studying the individual, International Journal of Behavioral Development . | spa |
| dc.relation.references | Geweke, J. (1977). The dynamic factor analysis of economic timeseries models, Latent variables in socio-economic models pp. 365–383. | spa |
| dc.relation.references | Graybill, F. A. F. A. (1983). Matrices with Applications in Statistics, Wadsworth statistics/probability series, second edn, Wadsworth International Group, Belmont, CA, USA. | spa |
| dc.relation.references | Hallin, M. & Lippi, M. (2013). Factor models in high-dimensional time series?a timedomain approach, Stochastic Processes and their Applications 123(7): 2678 – 2695. | spa |
| dc.relation.references | Hallin, M. & Liska, R. (2007). Determining the number of factors in the general dynamic factor model, Journal of the American Statistical Association 102(603-617). | spa |
| dc.relation.references | Hindrayanto, I., Koopman, S. J. & Ooms, M. (2010). Exact maximum likelihood estimation for non-stationary periodic time series models, Computational Statistics & Data Analysis 54: 2641–2654. | spa |
| dc.relation.references | Hu, Y.-P. (2005). Identifying the time-effect factors of multiple time series, Journal of Forecasting 24(379-387). | spa |
| dc.relation.references | Hu, Y.-P. (2011). Likelihood function and canonical correlation analysis of the Pe˜na-Box model, Communications in Statistics-Theory and Methods 40(1453-1467). | spa |
| dc.relation.references | Hu, Y.-P. & Chou, R.-J. (2003). A dynamic factor model., Journal ofTime Series Analysis 24(5): 529–538. | spa |
| dc.relation.references | Hu, Y.-P. & Chou, R.-J. (2004). On the Pe˜na-Box model, Journal ofTime Series Analysis 25(811-830). | spa |
| dc.relation.references | Hu, Y.-P. & Chou, R.-J. (2008). A generalized time-effect factor model and its application: recovering trend of temperature by pollen data, Environmetrics 19(5): 439–451. | spa |
| dc.relation.references | Huang, J. Z., Liu, N., Pourahmadi, M. & Liu, L. (2006). Covariance matrix selection and estimation via penalised normal likelihood, Biometrika 93(1): 85–98. | spa |
| dc.relation.references | Johnstone, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis, The Annals of Statistics 29(2): 295–327. | spa |
| dc.relation.references | Jungbacker, B. & Koopman, S. J. (2015). Likelihood-based dynamic factor analysis for measurement and forecasting, The Econometrics Journal 18(2): C1–C21. | spa |
| dc.relation.references | Koopman, S. J. & Durbin, J. (2000). Fast filtering and smoothing for multivariate state space models., Journal of Time Series Analysis 21(3): 281–296. | spa |
| dc.relation.references | Lam, C. & Yao, Q. (2012). Factor modeling for high-dimensional time series: Inference for the number of factors, The Annals of Statistics 40(2): 694–726. | spa |
| dc.relation.references | Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis, Springer Publishing Company. | spa |
| dc.relation.references | Marchenko, V. & Pastur, L. (1967). Distributions of eigenvalues of some sets of random matrices, Math. USSR-Sb 1: 507–536. | spa |
| dc.relation.references | Martínez, W. O., Nieto, F. H. & Poncela, P. (2013). Choosing a dynamic common factor as a coincident index, Reporte Interno de Investigación 25(1-26). | spa |
| dc.relation.references | Metaxoglou, K. & Smith, A. (2007). Maximun likelihood estimation of VARMA models using a state-space EM algorithm, Journal of Time Series Analysis 28(5): 666–685. | spa |
| dc.relation.references | Nieto, F. H., Peña, D. & Saboyá, D. (2016). Common seasonality in multivariate time series, Statistica Sinica 26(4): 1389–1410. | spa |
| dc.relation.references | Onatski, A. (2009). Testing hypotheses about the number of factors in large factor models, Econometrica 77(5): 1447–1479. | spa |
| dc.relation.references | Onatski, A. (2010). Determining the number of factors from empirical distribution of eigenvalues, The Review of Economics and Statistics 72(4): 1004–1016. | spa |
| dc.relation.references | Onatski, A. (2012). Asymptotics of the principal components estimator of large factor models with weakly influential factors, Journal of Econometrics 168(2): 244 – 258. | spa |
| dc.relation.references | Paul, D. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model, Statistica Sinica pp. 1617–1642. | spa |
| dc.relation.references | Peña, D. (2002). Análisis de datos multivariantes, McGraw-Hill/Interamericana de España. | spa |
| dc.relation.references | Peña, D. & Box, G. E. P. (1987). Identifying a simplifying structure in time series, Journal of the American Statistical Association 82(836-843). | spa |
| dc.relation.references | Peña, D. & Poncela, P. (2006). Dimension reduction in multivariate time series, in N. Balakrishnan, J. Sarabia & E. Castillo (eds), Advances in Distribution Theory, Order Statistics, and Inference, Statistics for Industry and Technology, Birkhäuser Boston, pp. 433–458. | spa |
| dc.relation.references | Peña, D. & Poncela, P. (2006). Nonstationary dynamic factor analysis, Journal of Statistical Planning and Inference 136(1237-1257). | spa |
| dc.relation.references | Peña, D. & Yohai, V. J. (2016). Generalized dynamic principal components, Journal of the American Statistical Association 111(515): 1121–1131. | spa |
| dc.relation.references | R Core Team (2019). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. URL: https://www.R-project.org/ | spa |
| dc.relation.references | Ram, N., Brose, A., Molenaar, P. C. et al. (2013). Dynamic factor analysis: Modeling person-specific process, The Oxford handbook of quantitative methods 2: 441–457. | spa |
| dc.relation.references | Reichel, L. & Trefethen, L. N. (1992). Eigenvalues and pseudo-eigenvalues of toeplitz matrices, Linear algebra and its applications 162: 153–185. | spa |
| dc.relation.references | Reinsel, G. C. (1997). Elements of Multivariate Time Series Analysis, second edi edn, Springer-Verlag. | spa |
| dc.relation.references | Resnick, S. (2005). A probability path, Birkhäuser. | spa |
| dc.relation.references | Rothman, A. J., Bickel, P. J., Levina, E., Zhu, J. et al. (2008). Sparse permutation invariant covariance estimation, Electronic Journal of Statistics 2: 494–515. | spa |
| dc.relation.references | Soshnikov, A. (2002). A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices, Journal of Statistical Physics 108(5-6): 1033– 1056. | spa |
| dc.relation.references | Stock, J. H. & Watson, M. W. (1991). A probability model of the coincident economic indicators, in: G. Moore and K. Lahiri, eds., The Leading Economic Indicators: New Approaches and Forecasting Records (Cambridge University Press, Cambridge) . | spa |
| dc.relation.references | Stock, J. H. & Watson, M. W. (2002). Macroeconomic forecasting using diffusion indexes, Journal of Business & Economic Statistics 20(2): 147–162. | spa |
| dc.relation.references | Stock, J. & Watson, M. (2016). Dynamic factor models, factor-augmented vector autoregressions, and structural vector autoregressions in macroeconomics, in J. B. Taylor & H. Uhlig (eds), Handbook of macroeconomics, Vol. 2 of Handbook of Macroeconomics, Elsevier, chapter 8, pp. 415 – 525. | spa |
| dc.relation.references | Tanaka, K. (2017). Time Series Analysis: Nonstationary and Noninvertible Distribution Theory, John Wiley & Sons. | spa |
| dc.relation.references | Tiao, G. C. & Tsay, R. S. (1989). Model specification in multivariate time series, Journal of the Royal Statistical Society. Series B (Methodological) 51(157-213). | spa |
| dc.relation.references | Tyler, D. E. et al. (1983). The asymptotic distribution of principal component roots under local alternatives to multiple roots, The Annals of Statistics 11(4): 1232–1242. | spa |
| dc.relation.references | Venables, W. N. & Ripley, B. D. (2002). Modern Applied Statistics with S, fourth edn, Springer, New York. | spa |
| dc.relation.references | Wu, W. B. & Pourahmadi, M. (2009). Banding sample autocovariance matrices of stationary processes, Statistica Sinica pp. 1755–1768. | spa |
| dc.rights | Derechos reservados - Universidad Nacional de Colombia | spa |
| dc.rights.accessrights | info:eu-repo/semantics/openAccess | spa |
| dc.rights.license | Atribución-NoComercial 4.0 Internacional | spa |
| dc.rights.spa | Acceso abierto | spa |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/4.0/ | spa |
| dc.subject.ddc | 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas | spa |
| dc.subject.proposal | Canonical correlation | eng |
| dc.subject.proposal | Correlación canónica | spa |
| dc.subject.proposal | Estacionalidad común | spa |
| dc.subject.proposal | Common seasonality | eng |
| dc.subject.proposal | Factores comunes dinámicos | spa |
| dc.subject.proposal | Dynamic common factors | eng |
| dc.subject.proposal | Series de tiempo multivariadas | spa |
| dc.subject.proposal | Multivariate time series | eng |
| dc.title | Análisis de factores comunes dinámicos en presencia de procesos de ruido autocorrelacionados | spa |
| dc.title.alternative | Analysis of dynamic common factors in the presence of autocorrelated noise-processes | spa |
| dc.type | Trabajo de grado - Doctorado | spa |
| dc.type.coar | http://purl.org/coar/resource_type/c_db06 | spa |
| dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | spa |
| dc.type.content | Text | spa |
| dc.type.driver | info:eu-repo/semantics/doctoralThesis | spa |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | spa |
| oaire.accessrights | http://purl.org/coar/access_right/c_abf2 | spa |