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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.45 no.1 Bogotá Jan./June 2022 Epub Jan 17, 2022
https://doi.org/10.15446/rce.v45n1.92965
Artículos originales de investigación
Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study
Datos atípicos aditivos en modelos autorregresivos de umbrales: un estudio de simulación
1 DEPARTMENT OF STATISTICS, FACULTY OF SCIENCES, UNIVERSIDAD NACIONAL DE COLOMBIA, BOGOTÁ D.C., COLOMBIA
The effect of additive outlier observations is investigated in adapting a non-linearity test and a robust estimation method for the autoregressive coefficients from SETAR(self-exciting threshold autoregressive) models to open-loop models. TAR (threshold autoregressive). Through a Monte Carlo experiment, the power and size of the non-linearity test are studied. Regarding the estimation, the bias and the mean square error ratio between the robust estimator and the least-squares estimator are compared. Additionally, the approximation of the GM estimators' empirical distribution to the univariate normal distribution is evaluated together with the coverage levels of the asymptotic confidence intervals. The results indicate that the adapted non-linearity test has higher power than that based on least squares and does not present distortions in size under the presence of additive outliers. On the other hand, the robust estimation method for autoregressive coefficients exceeds the least-squares one in terms of the mean square error in the presence of this type of observations. These results were analogous to those obtained for SETAR models. Finally, the use of the non-linearity test and the estimation method are illustrated through two real examples.
Key words: additive outliers; open-loop TAR models; generalized method (GM) estimator; nonlinear time series
Se investiga el efecto de observaciones atípicas aditivas en la adaptación de una prueba de no linealidad y un método de estimación robusto para los coeficientes autorregresivos de modelos SETAR(self-exciting threshold autoregressive) a modelos open-loop TAR(threshold autoregressive). A través de un experimento Monte Carlo se estudia la potencia y el tamaño de la prueba de no linealidad. Respecto a la estimación, se compara el sesgo y la razón de error cuadrático medio entre el estimador robusto y el de mínimos cuadrados. Adicionalmente, se evalúa la aproximación de la distribución empírica de los estimadores GM de los coeficientes a la distribución normal univariada junto a los niveles de cobertura de los intervalos de confianza asintóticos. Los resultados indican que la prueba de no linealidad adaptada presenta una potencia superior a la basada en mínimos cuadrados y no presenta distorsiones en el tamaño bajo la presencia de datos atípicos aditivos. Por otro lado, el método de estimación robusto para los coeficientes autorregresivos supera al de mínimos cuadrados en términos de error cuadrático medio bajo la presencia de este tipo de observaciones. Estos resultados fueron análogos a los obtenidos para modelos SETAR. Finalmente, se ilustra a través de dos ejemplos reales el uso de la prueba de no linealidad y el método de estimación.
Palabras clave: datos atípicos aditivos; modelos open-loop TAR; estimadores GM; series de tiempo no lineales
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Received: January 2021; Accepted: July 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
