Regresión beta usando cópulas gaussianas para analizar series de tiempo
Date
2023-01-11
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Pontificia Universidad Católica del Perú
Abstract
Este trabajo presenta una alternativa para analizar series de tiempo que se encuentran
restringidas al intervalo (0; 1). Se detalla el modelo propuesto Masarotto y Varin (2012) y
Guolo y Varin (2014), el cual permite capturar los efectos producidos por covariables a través
de una regresión beta y adicionalmente, con el empleo de cópulas permite modelar la dependencia
temporal mediante un proceso de autorregresivo de medias móviles. Como ventaja de
la aplicación de este modelo se tiene que evita la necesidad de transformar la variable dependiente,
así como también evita someterla al cumplimiento de diversos supuestos como los
de normalidad y estacionariedad. Además, permite diferenciar los efectos de las covariables
y de la dependencia temporal, lo cual coadyuva a mejorar el análisis de los resultados. Se
realizó una aplicación a la tasa de desempleo desde enero de 2003 hasta octubre de 2019 en
Lima Metropolitana y debido a la distribución que presenta esta variable se usó un modelo
de regresión beta usando cópulas gaussianas. Para la estimación se incluyó el logaritmo del
índice del PBI, así como un componente de estacionalidad anual como covariables y para
tomar en cuenta la dependencia temporal se incorporó un proceso autorregresivo de medias
móviles ARMA(1; 1) a través de una cópula gaussiana.
This work presents an alternative to analyze time series restricted to the interval (0; 1). This model was proposed by Masarotto y Varin (2012) and Guolo y Varin (2014), which allows to capture covariates effects through a beta regression and additionally allows to model the temporal dependence by copulas through an autoregressive moving averages process. As an advantage of the application of this model, it is not necessary to transform the dependent variable or subject to compliance the assumptions such as normality and stationarity. Also, it allows to differentiate the effects of the covariates and of the temporal dependence, which helps to improve the analysis of results. An application to the unemployment rate from January 2003 to October 2019 in Metropolitan Lima was implemented and due to the distribution presented by this variable it was used a gaussian copula beta regression model. The model includes the logarithm of the GDP index and annual seasonality component as covariates, and to take into account the temporal dependence it was included an autoregressive moving averages process ARMA(1; 1) through a gaussian copula.
This work presents an alternative to analyze time series restricted to the interval (0; 1). This model was proposed by Masarotto y Varin (2012) and Guolo y Varin (2014), which allows to capture covariates effects through a beta regression and additionally allows to model the temporal dependence by copulas through an autoregressive moving averages process. As an advantage of the application of this model, it is not necessary to transform the dependent variable or subject to compliance the assumptions such as normality and stationarity. Also, it allows to differentiate the effects of the covariates and of the temporal dependence, which helps to improve the analysis of results. An application to the unemployment rate from January 2003 to October 2019 in Metropolitan Lima was implemented and due to the distribution presented by this variable it was used a gaussian copula beta regression model. The model includes the logarithm of the GDP index and annual seasonality component as covariates, and to take into account the temporal dependence it was included an autoregressive moving averages process ARMA(1; 1) through a gaussian copula.
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Keywords
Análisis de series cronológicas, Análisis de regresión, Desempleo urbano--Perú--Lima Metropolitana
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