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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.44 no.1 Bogotá Jan./June 2021 Epub Feb 24, 2021
https://doi.org/10.15446/rce.v44n1.84816
Artículos originales de investigación
On a New Procedure for Identifying a Dynamic Common Factor Model
Sobre un nuevo procedimiento para identificar un modelo de factores comunes dinámicos
1Department of Industrial Engineering, Pontificia Universidad Javeriana, Bogotá, Colombia
2Department of Statistics, Universidad Nacional de Colombia, Bogotá, Colombia
3Department of Statistics, Universidad Carlos III de Madrid, Madrid, España
In the context of the exact dynamic common factor model, canonical correlations in a multivariate time series are used to identify the number of latent common factors. In this paper, we establish a relationship between canonical correlations and the autocovariance function of the factor process, in order to modify a pre-established statistical test to detect the number of common factors. In particular, the test power is increased. Additionally, we propose a procedure to identify a vector ARMA model for the factor process, which is based on the so-called simple and partial canonical autocorrelation functions. We illustrate the proposed methodology by means of some simulated examples and a real data application.
Key words: Canonical correlations; Dynamic common factors; Multivariate time series
En el contexto del modelo exacto de factores comunes dinámicos, las correlaciones canónicas en series de tiempo multivariadas son usadas para identificar el número de factores latentes. En este artículo, establecemos la relación entre correlación canónica y la función de autocovarianza del proceso de los factores, con el fin de modificar una prueba estadística diseñada para identificar el número de factores comunes. En particular, se incrementa la potencia de la prueba. Adicionalmente, proponemos un procedimiento para identificar el modelo VARMA para el proceso de los factores, el cual está basado en lo que denominamos las funciones de autocorrelación simple y parcial. Ilustramos la metodología propuesta por medio de ejemplos simulados y una aplicación con datos reales.
Palabras clave: Correlación canónica; Factores comunes dinámicos; Series de tiempo multivariadas
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