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

Autores/as

  • Rosa Badillo Amador Departamento de Economía Universidad Politécnica de Cartagena
  • Jorge Belaire Franch Departamento de Fundamentos del Análisis Económico Universidad de Valencia
  • Carmelo Reverte Maya Departamento de Economía Financiera y Contabilidad Universidad Politécnica de Cartagena

Palabras clave:

Unit roots, structural breaks, Dickey-Fuller tests, raíces unitarias, cambios estructurales, test Dickey-Fuller

Resumen

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.

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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.

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Citas

Banerjee, A., Lumsdaine, R.L. and Stock, J.H. (1992) Recursive and sequential tests of the unit-root and trend-break hypotheses: Theory and international evidence, Journal of Business & Economic Statistics, 10, 271–87.

Christiano, L. J. (1992) Searching for a break in GNP, Journal of Business and Economic Statistics, 10, 237–250.

Dickey, D. and Fuller, W. (1979) Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Satistical Association, 74, 427–431.

Fuller, W. A. (1976) Introduction to statistical time series. New York, Willey.

Granger, C.W.J. and Newbold, P. (1974) Spurious regressions in Econometrics, Journal of Econometrics, 2, 111–120.

Leybourne, S., Mills, T. and Newbold, P. (1998) Spurious rejections by DF tests in the presence of a break under the null, Journal of Econometrics, 87, 191–203.

Nelson, C.R. and Plosser C.I. (1982) Trends and random walks in macroeconomic time series: Some evidence and implications, Journal of Monetary Economics, 10, 139–162

Perron, P. (1989) The great crash, the oil price shock and the unit root hypothesis, Econometrica, 57, 1361-1401.

Perron, P. (1994) Trend, unit root and structural change in macroeconomic time series. In Rao, B. B. (ed), Cointegration for the Applied Economists. MacMillan, New York, NY, 113–146.

Perron, P. (1997) Further evidence on breaking trend functions in macroeconomic variables, Journal of Econometrics, 80, 355–385.

Perron, P., Vogelsang, T. J., (1992) Nonstationarity and level shifts with an application to purchasing power parity, Journal of Business and Economic Statistics 10, 301–320.

Vogelsang, T. J., Perron, P. (1998) Additional tests for a unit root allowing for a break in the trend function at an unknown time, International Economic Review 39(4), 1073–1100.

Yule, G.U. (1926) Why do we sometimes get nonsense correlations between time series? A study in sampling and the nature of time series, Journal of the Royal Statistical Society, 89, 1–64.

Zivot, E., Andrews, D.W.K., (1992) Further evidence on the Great Crash, the oil price shock, and the unit root hypothesis, Journal of Business and Economic Statistics 10, 251–270.

Publicado

2016-11-04

Cómo citar

Badillo Amador, R., Belaire Franch, J., & Reverte Maya, C. (2016). 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. Revista De Métodos Cuantitativos Para La Economía Y La Empresa, 9, Páginas 3 a 16. Recuperado a partir de https://www.upo.es/revistas/index.php/RevMetCuant/article/view/2145

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