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The discontinuous trend unit root test when the break point is misspecified

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  • Morimune, Kimio
  • Nakagawa, Mitsuru

Abstract

Dickey and Fuller proposed some tests for the unit root hypothesis in uni-variate time series. [P. Perron, The great crash, the oil price shock, and the unit root hypothesis, Econometrica 57 (1989) 1361–1401] extended the t-ratio type unit root tests so that they allow for a break in the deterministic trend and/or in the intercept term. The purpose of the paper is to study by simulations the effect of a misspecified break point on the tests proposed by Perron. Further, the limits of the test statistics by Perron are derived under the assumption of a misspecified break point, and the accuracy of the limit formula is examined by simulation techniques. Finally, a test is proposed which jumps the break interval instead of a break point.

Suggested Citation

  • Morimune, Kimio & Nakagawa, Mitsuru, 1999. "The discontinuous trend unit root test when the break point is misspecified," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 417-427.
    • Handle: RePEc:eee:matcom:v:48:y:1999:i:4:p:417-427
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    References listed on IDEAS

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    1. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    2. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
    3. Perron, P, 1993. "Erratum [The Great Crash, the Oil Price Shock and the Unit Root Hypothesis]," Econometrica, Econometric Society, vol. 61(1), pages 248-249, January.
    4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    5. Montanes, Antonio, 1997. "Level shifts, unit roots and misspecification of the breaking date," Economics Letters, Elsevier, vol. 54(1), pages 7-13, January.
    6. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
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