Escudo de la República de Colombia
Sistema Nacional de Biliotecas - Repositorio Institucional Universidad Nacional de Colombia Biblioteca Digital - Repositorio Institucional UN Sistema Nacional de Bibliotecas UN

Tendencia aleatoria o determinística: una nueva prueba basada en la teoría tradicional

Castaño, Elkin and Martínez, Jorge (2011) Tendencia aleatoria o determinística: una nueva prueba basada en la teoría tradicional. Revista Colombiana de Estadística; Vol. 32, núm. 2 (2009); 301-331 Revista Colombiana de Estadística; Vol. 32, núm. 2 (2009); 301-331 0120-1751 .

Texto completo

[img]
Vista previa
PDF
298kB
[img] HTML
12kB

URL oficial: http://revistas.unal.edu.co/index.php/estad/articl...

Resumen

Several procedures to test the null hypothesis on the random or deterministic origin of the trend in a time series are found in the specialized literature. Most of these tests are based on the analysis of the unit roots of the autoregressive or moving average operators. The procedures are based on the nonstandard theory associated to a Wiener process. In this paper it is proposed a test that uses the autocorrelation function (ACF) of the residuals considering the null hypothesis H0 : Z_{t} = β_{0} + Z_{t-1} + a_{t}, and the alternative hypothesis H1 : Z_{t} = β_{0} + β_{1}t+a_{t}. The distribution of the test statistics for finite sample sizes and the asymptotic approximation are obtained using the usual theory, assuming that at is a gaussian white noise. The procedure is generalized for the case where at is a correlated white noise. The results obtained using simulation show that the proposed test has in general high power and specially when it is compared the well known Dicker-Fuller Augmented test (ADF), in the case when the roots of the autoregressive or moving average operators are close to one. The proposed procedure has also better approximation to the nominal test size when it is also compared with the ADF., Several procedures to test the null hypothesis on the random or deterministic origin of the trend in a time series are found in the specialized literature. Most of these tests are based on the analysis of the unit roots of the autoregressive or moving average operators. The procedures are based on the nonstandard theory associated to a Wiener process. In this paper it is proposed a test that uses the autocorrelation function (ACF) of the residuals considering the null hypothesis H0 : Z_{t} = β_{0} + Z_{t-1} + a_{t}, and the alternative hypothesis H1 : Z_{t} = β_{0} + β_{1}t+a_{t}. The distribution of the test statistics for finite sample sizes and the asymptotic approximation are obtained using the usual theory, assuming that at is a gaussian white noise. The procedure is generalized for the case where at is a correlated white noise. The results obtained using simulation show that the proposed test has in general high power and specially when it is compared the well known Dicker-Fuller Augmented test (ADF), in the case when the roots of the autoregressive or moving average operators are close to one. The proposed procedure has also better approximation to the nominal test size when it is also compared with the ADF.

Tipo de documento:Artículo - Article
Palabras clave:tendencia aleatoria, tendencia determinística, función de autocorrelación, modelo ARMA, raíz unitaria, prueba de Dickey y Fuller aumentada, Stochastic trend, Deterministic model, Autocorrelation function, ARMA model, Unit root, Dickey-Fuller test
Unidad administrativa:Revistas electrónicas UN > Revista Colombiana de Estadística
Código ID:30829
Enviado por : Dirección Nacional de Bibliotecas STECNICO
Enviado el día :30 Junio 2014 14:05
Ultima modificación:18 Agosto 2014 19:12
Ultima modificación:18 Agosto 2014 19:12
Exportar:Clic aquí
Estadísticas:Clic aquí
Compartir:

Solamente administradores del repositorio: página de control del ítem

Vicerrectoría de Investigación: Número uno en investigación
Indexado por:
Indexado por Scholar Google WorldCat DRIVER Registry of Open Access Repositories OpenDOAR Metabiblioteca BDCOL OAIster Red de repositorios latinoamericanos DSpace BASE Open archives La referencia Colombiae Open Access Theses and Dissertations Tesis latinoamericanas CLACSO
Este sitio web se ve mejor en Firefox