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Residual Augmented Fourier ADF Unit Root Test

Author

Listed:
  • Yilanci, Veli
  • Aydin, Mücahit
  • Aydin, Mehmet

Abstract

This paper proposes a residual-based unit root test in the presence of smooth structural changes approximated by a Fourier function. While Fourier Augmented Dickey Fuller test that introduced by Enders and Lee (2012a) allows smooth changes of the unknown form, the Residual Augmented Least Squares procedure use additional higher moment information found in non-normal errors. The test offers a simple way to accommodate an unknown number and form of structural breaks and have good size and power properties in the case of non-normal errors.

Suggested Citation

  • Yilanci, Veli & Aydin, Mücahit & Aydin, Mehmet, 2019. "Residual Augmented Fourier ADF Unit Root Test," MPRA Paper 96797, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:96797
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    File URL: https://mpra.ub.uni-muenchen.de/96797/1/MPRA_paper_96797.pdf
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    References listed on IDEAS

    as
    1. Hidetaka I. Ohara, 1999. "A Unit Root Test With Multiple Trend Breaks: A Theory and an Application to US and Japanese Macroeconomic Time-Series," The Japanese Economic Review, Japanese Economic Association, vol. 50(3), pages 266-290, September.
    2. Im, Kyung So & Schmidt, Peter, 2008. "More efficient estimation under non-normality when higher moments do not depend on the regressors, using residual augmented least squares," Journal of Econometrics, Elsevier, vol. 144(1), pages 219-233, May.
    3. Gilberto Libanio, 2005. "Unit roots in macroeconomic time series: theory, implications, and evidence," Nova Economia, Economics Department, Universidade Federal de Minas Gerais (Brazil), vol. 15(3), pages 145-176, September.
    4. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    5. Junsoo Lee & Mark C. Strazicich, 2013. "Minimum LM unit root test with one structural break," Economics Bulletin, AccessEcon, vol. 33(4), pages 2483-2492.
    6. Lanne, Markku & Lutkepohl, Helmut, 2002. "Unit root tests for time series with level shifts: a comparison of different proposals," Economics Letters, Elsevier, vol. 75(1), pages 109-114, March.
    7. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    8. Saikkonen, Pentti & Lütkepohl, Helmut, 2002. "Testing For A Unit Root In A Time Series With A Level Shift At Unknown Time," Econometric Theory, Cambridge University Press, vol. 18(2), pages 313-348, April.
    9. 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.
    10. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
    11. 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.
    12. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    13. Paulo M. M. Rodrigues & A. M. Robert Taylor, 2012. "The Flexible Fourier Form and Local Generalised Least Squares De-trended Unit Root Tests-super-," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(5), pages 736-759, October.
    14. Walter Enders & Junsoo Lee, 2012. "A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(4), pages 574-599, August.
    15. Junsoo Lee & Mark C. Strazicich, 2003. "Minimum Lagrange Multiplier Unit Root Test with Two Structural Breaks," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1082-1089, November.
    16. Markku Lanne & Helmut Lütkepohl & Pentti Saikkonen, 2002. "Comparison of unit root tests for time series with level shifts," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 667-685, November.
    17. Enders, Walter & Lee, Junsoo, 2012. "The flexible Fourier form and Dickey–Fuller type unit root tests," Economics Letters, Elsevier, vol. 117(1), pages 196-199.
    18. Clemente, Jesus & Montanes, Antonio & Reyes, Marcelo, 1998. "Testing for a unit root in variables with a double change in the mean," Economics Letters, Elsevier, vol. 59(2), pages 175-182, May.
    19. Ralf Becker & Walter Enders & Junsoo Lee, 2006. "A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 381-409, May.
    20. repec:bla:jtsera:v:19:y:1998:i:1:p:83-97 is not listed on IDEAS
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    More about this item

    Keywords

    Non-normal errors; Fourier Function; Unit root.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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