Abstract

CALDERON, SERGIO  and  CALLAMAD, DANIEL ORDOÑEZ. Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study. Rev.Colomb.Estad. [online]. 2022, vol.45, n.1, pp.1-40.  Epub Jan 17, 2022. ISSN 0120-1751.  https://doi.org/10.15446/rce.v45n1.92965.

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.

Keywords : additive outliers; open-loop TAR models; generalized method (GM) estimator; nonlinear time series.

        · abstract in Spanish     · text in English     · English ( pdf )