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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.38 no.1 Bogotá Jan./July 2015
https://doi.org/10.15446/rce.v38n1.48813
http://dx.doi.org/10.15446/rce.v38n1.48813
1Universidad Santo Tomás, Facultad de Estadística, Bogotá, Colombia. Professor. Email: hanwenzhang@usantotomas.edu.co
2Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. Professor. Email: fhnietos@unal.edu.co
This paper considers the modeling of the threshold autoregressive (TAR) process, which is driven by a noise process that follows a Students t-distribution. The analysis is done in the presence of missing data in both the threshold process {Zt} and the interest process {Xt}. We develop a three-stage procedure based on the Gibbs sampler in order to identify and estimate the model. Additionally, the estimation of the missing data and the forecasting procedure are provided. The proposed methodology is illustrated with simulated and real-life data.
Key words: Bayesian Statistics, Gibbs Sampler, Missing Data, Forecasting, Time Series, Threshold Autoregressive Model.
En este trabajo consideramos el modelamiento de los modelos autoregresivos de umbrales (TAR) con datos faltantes tanto en la serie de umbrales como la serie de interés cuando el proceso del ruido blanco sigue una distribución t de student. Desarrollamos un procedimiento de tres etapas basado en el muestreador de Gibbs para identificar y estimar el modelo, además de la estimación de los datos faltantes y el procedimiento para el pronóstico. La metodología propuesta fue aplicada a datos simulados y datos reales.
Palabras clave: datos faltantes, estadística Bayesiana, modelo autoregresivo de umbrales, muestreador de Gibbs, pronóstico, series de tiempo.
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References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv38n1a13,
AUTHOR = {Zhang, Hanwen and Nieto, Fabio H.},
TITLE = {{TAR Modeling with Missing Data when the White Noise Process Follows a Student's t-Distribution}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2015},
volume = {38},
number = {1},
pages = {239-266}
} 