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The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis

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  • Montañés, Antonio
  • Reyes, Marcelo

Abstract

This paper considers the behaviour of the Dickey-Fuller tests when the variable being studied is generated according to Perron's (1989) crash hypothesis. We show that these statistics tend towards the Dickey-Fuller distributions under the null hypothesis and diverge towards -[infinity] under the alternative.

Suggested Citation

  • Montañés, Antonio & Reyes, Marcelo, 1999. "The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 81-89, March.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:1:p:81-89
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    1. Perron, Pierre & Vogelsang, Timothy J., "undated". "Level Shifts and Purchasing Power Parity," Instructional Stata datasets for econometrics levshift, Boston College Department of Economics.
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    7. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    8. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
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    Cited by:

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    2. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
    3. Montañés, Antonio & Reyes, Marcelo, 2000. "Structural breaks, unit roots and methods for removing the autocorrelation pattern," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 401-409, July.
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    5. Sen, Amit, 2001. "Behaviour of Dickey-Fuller F-tests under the trend-break stationary alternative," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 257-268, December.
    6. Sen, Amit, 2008. "Behaviour of Dickey-Fuller tests when there is a break under the unit root null hypothesis," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 622-628, April.
    7. Amit Sen, 2007. "On the Distribution of the Break-Date Estimator Implied by the Perron-Type Statistics When the Form of Break is Misspecified," Economics Bulletin, AccessEcon, vol. 3(6), pages 1-19.
    8. Brodsky, Boris, 2008. "Structural Changes and Unit Roots: Distinguishing Models of Nonstationary Time Series," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 11(3), pages 52-63.
    9. Artur C. B. da Silva Lopes & Antonio Montanes, 2005. "The Behavior Of Hegy Tests For Quarterly Time Series With Seasonal Mean Shifts," Econometric Reviews, Taylor & Francis Journals, vol. 24(1), pages 83-108.
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