1Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. Profesor titular. Email: fhnietos@unal.edu.co
2Universidad Nacional de Colombia, Facultad de Economía, Bogotá, Colombia. Profesora auxiliar. Email: nmhoyosg@unal.edu.co
Nowadays, procedures for testing the null hypothesis of linearity of a (univariate or multivariate) stochastic process are well known, almost all of them based on the assumption that their paths (i.e. observed time series) are complete. This paper describes an approach for testing this null hypothesis in the presence of missing data, using an extension of one of the test statistics used in the literature. The alternative hypothesis is that the univariate stochastic process of interest follows a threshold autoregressive (TAR) model. It is found that if the missing-data percentage is low, the null distribution of the proposed test statistic is maintained; while if it is high, it is not. A threshold value for the missing-data percentage is detected, which can be utilized in practice.
Key words: Linearity test, Missing data, Nonlinear time series, Threshold autoregressive model.
Las pruebas estadísticas que se conocen actualmente para examinar la hipótesis nula de linealidad de un proceso estocástico (univariado o multivariado) están basadas, casi todas, en el supuesto de que las series temporales observadas son completas. En este trabajo, se presenta un nuevo procedimiento para examinar esta hipótesis nula, en presencia de datos faltantes, el cual es una extensión de un método muy citado en la literatura. La hipótesis alternativa especifica que el proceso estocástico de interés obedece a un modelo autoregresivo de umbrales (TAR). Se encuentra que si el porcentaje de observaciones faltantes es bajo, la distribución nula de la estadística de prueba se mantiene; en otro caso no. El estudio arroja un valor umbral para este porcentaje, el cual puede ser usado en la práctica.
Palabras clave: datos faltantes, modelos autoregresivos de umbrales, prueba de linealidad, series de tiempo no linales.
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv34n1a04, ]]>
AUTHOR = {Nieto, Fabio H. and Hoyos, Milena},
TITLE = {{Testing Linearity against a Univariate TAR Specification in Time Series with Missing Data}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2011},
volume = {34},
number = {1},
pages = {73-94}
}