Published

2022-01-01

Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study

Datos atípicos aditivos en modelos autorregresivos de umbrales: un estudio de simulación

Keywords:

Nonlinear time series (en)
Modelos open-loop TAR, Estimadores GM (es)

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Authors

  • Sergio Calderon Universidad Nacional de Colombia
  • Daniel Ordoñez Callamad Universidad Nacional de Colombia

The effect of additive outliers is studied on an adapted non-linearity test and a robust estimation method for autoregressive coefficients in open-loop TAR (threshold autoregressive) models. Through a Monte Carlo experiment, the power and size of the non-linearity test are studied. Regarding the estimation method, the bias and ratio of mean squared errors are compared between the robust estimator and least squares. Simulation exercises are carried out for different percentages of contamination and the proportion of observations on each model regime. Furthermore, the approximation of the univariate normal distribution to the empirical distribution of estimated coefficients is analyzed along with the coverage level of asymptotic confidence intervals for the parameters. Results show that the adapted non-linearity test does not have size distortions, and it has a superior power than its least-squares counterpart when additive outliers are present. On the other hand, the robust estimation method for the autoregressive coefficients has a better mean squared error than least-squares when this type of observations are present. Lastly, the use of the non-linearity test and the estimation method are illustrated through a real example.

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 autoregresivos en modelos open-loop TAR (threshold autoregres- sive). 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 llevan a cabo ejercicios de simulación para diferentes porcentajes de contaminación, proporción de observaciones en cada régimen del modelo y se evalúa la aproximación de la distribución empírica de los coeficientes estimados por medio de la distribución normal univariada junto a los niveles de cobertura de los intervalos de confianza asintóticos para los parámetros. 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 autoregresivos supera al de mínimos cuadrados en términos de error cuadrático medio bajo la presencia de este tipo de observaciones. Finalmente, se ilustra a través de un ejemplo real el uso de la prueba de no linealidad y el método de estimación en la práctica.

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