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Spurious Rejections by Dickey-Fuller Tests in the Presence of an Endogenously Determined Break under the Null = Rechazos espurios de los test de Dickey-Fuller en presencia de una ruptura bajo la hipótesis nula endógenamente determinada

Author

Listed:
  • Badillo Amador, Rosa

    () (Departamento de Economía, Universidad Politécnica de Cartagena (España))

  • Belaire Franch, Jorge

    () (Departamento de Fundamentos del Análisis Económico, Universidad de Valencia (España))

  • Reverte Maya, Carmelo

    () (Departamento de Economía Financiera y Contabilidad, Universidad Politécnica de Cartagena (España))

Abstract

Leybourne et al. (1998) have proved the possibility of a “converse Perron phenomenon” when conventional Dickey-Fuller tests are applied to determine the order of integration of a time series. That is, if the true generating process is I(1) but with a break, frequent spurious rejections of the null hypothesis can occur. Although Leybourne et al. (1998) suggest it would be appropriate to use procedures in which the break date was treated as endogenous, they consider it as exogenous. Thus, this paper analyses whether their results change when the structural break is identified endogenously, that is, if the break point is gleaned from the data. In this sense, applying a recursive tDF test to a unit root process which has a break in its level, there is no virtually evidence of the `converse Perron phenomenon'. For the rest of the endogeneization procedures (i.e., rolling and sequential) and for the two types of breaks considered (in level or in drift), we find, in line with Leybourne et al. (1998), some distortion in the Dickey-Fuller tDF test size, which depends on the break size, the location of the break point in the sample and the sample size. Leybourne et al. (1998) muestran el cumplimiento del denominado “fenómeno inverso de Perron" cuando se aplican los test convencionales de Dickey-Fuller para determinar el orden de integración de una serie temporal. Este fenómeno consiste en que, si el verdadero proceso generador es I(1) pero con una ruptura, pueden producirse rechazos espurios frecuentes de la hipótesis nula. Aunque Leybourne et al. (1998) sugieren que sería apropiado utilizar procedimientos en los que la ruptura sea tratada como endógena, ellos la consideran como exógena. Así, este trabajo analiza si sus resultados cambian cuando la ruptura estructural se determina endógenamente, es decir, a partir de los datos. En este sentido, aplicando el procedimiento tDF recursivo a un proceso de raíz unitaria con una ruptura en el nivel, no encontramos prácticamente evidencia del “fenómeno inverso de Perron". Para el resto de procedimientos de endogeneización (rolling y secuencial) y para los dos tipos de rupturas considerados (en nivel o en deriva) encontramos, en línea con Leybourne et al. (1998), alguna distorsión en el tamaño del test tDF de Dickey-Fuller, la cual depende de la magnitud de la ruptura, de su ubicación en la muestra y del tamaño de la misma.

Suggested Citation

  • Badillo Amador, Rosa & Belaire Franch, Jorge & Reverte Maya, Carmelo, 2010. "Spurious Rejections by Dickey-Fuller Tests in the Presence of an Endogenously Determined Break under the Null = Rechazos espurios de los test de Dickey-Fuller en presencia de una ruptura bajo la hipót," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 9(1), pages 3-16, June.
  • Handle: RePEc:pab:rmcpee:v:9:y:2010:i:1:p:3-16
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    Keywords

    unit roots; structural breaks; Dickey-Fuller tests; raíces unitarias; cambios estructurales; test Dickey-Fuller;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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