The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis. (English) Zbl 1087.62511

Montañés, Antonio; Reyes, Marcelo

Stat. Probab. Lett. 42, No. 1, 81-89 (1999).

Summary: This paper considers the behaviour of the Dickey-Fuller tests when the variable being studied is generated according to P. Perron’s crash hypothesis [Econometrica 57, No. 6, 1361–1401 (1989; Zbl 0683.62066)]. We show that these statistics tend towards the Dickey-Fuller distributions under the null hypothesis and diverge towards \(-\infty\) under the alternative.

MSC:

62P20	Applications of statistics to economics
91B84	Economic time series analysis
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)

Citations:

Zbl 0683.62066

References:

[2]	Banerjee, A.; Lumsdaine, R.; Stock, J., Recursive and sequential tests of the unit root and trend break hypothesis, theory and international evidence, J. Business Econom. Statist., 10, 271-287 (1992)
[3]	Christiano, L., Searching for a break in GNP, J. Bus. Econom. Statist., 10, 237-250 (1992)
[4]	Dickey, D. A.; Fuller, W. A., Distribution of the estimators for autoregressive time series with a unit root, J. Amer. Statist. Assoc., 74, 427-431 (1979) · Zbl 0413.62075
[6]	Fuller, W. A.; Hasza, D. P.; Goebel, J. J., Estimation of the parameters of stochastics difference equations, Ann. Statist., 9, 531-543 (1981) · Zbl 0499.62082
[7]	Montañés, A.; Reyes, M., Effect of a shift in the trend function on Dickey-Fuller unit root tests., Econom. Theory, 14, 355-363 (1998)
[8]	Perron, P., The great crash, the oil shock and the unit root hypothesis, Econometrica, 57, 1361-1402 (1989) · Zbl 0683.62066
[9]	Perron, P., Testing for a unit root in a time series with a changing mean, J. Bus. Econom. Statist., 8, 153-162 (1990)
[10]	Perron, P.; Vogelsang, T. J., Nonstationarity and level shifts with an application to purchasing power parity, J. Econom. Statist., 10, 301-320 (1992)
[11]	Rappoport, P.; Reichlin, L., Segmented trends and non-stationary time series, Econom. J., 99, 168-177 (1989)
[12]	Schwert, G. W., Tests for unit roots: A Monte Carlo investigation, J. Bus. Econom. Statist., 7, 147-159 (1989)
[13]	Zivot, E.; Andrews, D. W.K., Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis, J. Bus. Econom. Statist., 10, 251-270 (1992)