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Behaviour of Dickey-Fuller Unit Root Tests Under Trend Misspecification

Author

Listed:
  • Steve Leybourne

    (Nottingham)

  • Tae-Hwan Kim

    (Nottingham)

  • Paul Newbold

    (Nottingham)

Abstract

We analyse the case where a unit root test is based on a Dickey-Fuller regression whose only deterministic term is a fixed intercept. Suppose, however, as could well be the case, that the actual data generating process includes a broken linear trend. It is shown theoretically, and verified empirically, that under the I(1) null and I(0) alternative hypotheses the Dickey-Fuller test can display a wide range of different characteristics depending on the nature and location of the break.

Suggested Citation

  • Steve Leybourne & Tae-Hwan Kim & Paul Newbold, 2003. "Behaviour of Dickey-Fuller Unit Root Tests Under Trend Misspecification," Econometrics 0311008, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0311008
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    References listed on IDEAS

    as
    1. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    2. West, Kenneth D., 1987. "A note on the power of least squares tests for a unit root," Economics Letters, Elsevier, vol. 24(3), pages 249-252.
    3. Leybourne, Stephen J. & Newbold, Paul, 2000. "BEHAVIOR OF DICKEY–FULLER t-TESTS WHEN THERE IS A BREAK UNDER THE ALTERNATIVE HYPOTHESIS," Econometric Theory, Cambridge University Press, vol. 16(5), pages 779-789, October.
    4. Ayat, Leila & Burridge, Peter, 2000. "Unit root tests in the presence of uncertainty about the non-stochastic trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 71-96, March.
    5. 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.
    6. Pantula, Sastry G & Gonzalez-Farias, Graciela & Fuller, Wayne A, 1994. "A Comparison of Unit-Root Test Criteria," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 449-459, October.
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    Cited by:

    1. Ventosa-Santaularària, Daniel & Gómez, Manuel, 2006. "Inflation and Breaks: the validity of the Dickey-Fuller test," MPRA Paper 58773, University Library of Munich, Germany.
    2. Geetilaxmi MOHAPATRA & A. K. GIRI & Madhu SEHRAWAT, 2016. "Foreign aid, macroeconomic policies and economic growth nexus in India: An ARDL bounds testing approach," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(609), W), pages 183-202, Winter.
    3. Madhu Sehrawat & A.K. Giri, 2018. "Globalization, role of institutions and economic performance in Indian economy," Journal of Financial Economic Policy, Emerald Group Publishing Limited, vol. 11(1), pages 82-100, October.
    4. Muhammad Shahbaz & Faridul Islam, 2011. "Financial Development And Income Inequality In Pakistan: An Application Of Ardl Approach," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 36(1), pages 35-58, March.
    5. Jürgen Wolters & Uwe Hassler, 2006. "Unit Root Testing," Springer Books, in: Olaf Hübler & Jachim Frohn (ed.), Modern Econometric Analysis, chapter 4, pages 41-56, Springer.
    6. Waqar Khalid & Ahmad Nawaz & Lamya Mohamed Aly Gadou & Saqib Ullah Khan & Huri Gül Aybudak, 2025. "Examining short-run and long-run nexus between economic growth, financial development, energy consumption and environmental degradation: empirical evidence for the Environmental Kuznets Curve Hypothesis in Egypt," Asia-Pacific Journal of Regional Science, Springer, vol. 9(2), pages 479-511, June.
    7. Dagum, Estela Bee & Giannerini, Simone, 2006. "A critical investigation on detrending procedures for non-linear processes," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 175-191, March.
    8. Tursoy, Turgut & Faisal, Faisal, 2018. "The impact of gold and crude oil prices on stock market in Turkey: Empirical evidences from ARDL bounds test and combined cointegration," Resources Policy, Elsevier, vol. 55(C), pages 49-54.
    9. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    10. Geetilaxmi MOHAPATRA & A. K. GIRI & Madhu SEHRAWAT, 2016. "Foreign aid, macroeconomic policies and economic growth nexus in India: An ARDL bounds testing approach," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(4(609), W), pages 183-202, Winter.
    11. Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
    12. Ventosa-Santaulária, Daniel & Gómez-Zaldívar, Manuel, 2009. "Broken mean stationarity and the validity of the Dickey-Fuller test: the case of controlled inflation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 29(1), May.
    13. Juan Carlos Cuestas & Luis A. Gil-Alana & María Malmierca, 2022. "Credit-to-GDP ratios – non-linear trends and persistence: evidence from 44 OECD economies," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 50(3), pages 448-463, March.

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    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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