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Reducing the Size Distortion of the KPSS Test

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  • Eiji Kurozumi
  • Shinya Tanaka

Abstract

This paper proposes a new stationarity test based on the KPSS test with less size distortion. We extend the boundary rule proposed by Sul, Phillips and Choi (2005) to the autoregressive spectral density estimator and parametrically estimate the long-run variance. We also derive the finite sample bias of the numerator of the test statistic up to the 1/T order and propose a correction to the bias term in the numerator. Finite sample simulations show that the correction term effectively reduces the bias in the numerator and that the finite sample size of our test is close to the nominal one as long as the long-run parameter in the model satisfies the boundary condition.

Suggested Citation

  • Eiji Kurozumi & Shinya Tanaka, 2009. "Reducing the Size Distortion of the KPSS Test," Global COE Hi-Stat Discussion Paper Series gd09-085, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:ghsdps:gd09-085
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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd09-085.pdf
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    References listed on IDEAS

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    1. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    2. Kurozumi, Eiji, 2009. "Construction of Stationarity Tests with Less Size Distortions," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 50(1), pages 87-105, June.
    3. Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
    4. Harris, David & Leybourne, Stephen & McCabe, Brendan, 2007. "Modified Kpss Tests For Near Integration," Econometric Theory, Cambridge University Press, vol. 23(02), pages 355-363, April.
    5. Markku Lanne & Pentti Saikkonen, 2003. "Reducing size distortions of parametric stationarity tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 423-439, July.
    6. Josep Carrion-i-Silvestre & Andreu Sansó, 2006. "A guide to the computation of stationarity tests," Empirical Economics, Springer, vol. 31(2), pages 433-448, June.
    7. Saikkonen, Pentti & Luukkonen, Ritva, 1993. "Point Optimal Tests for Testing the Order of Differencing in ARIMA Models," Econometric Theory, Cambridge University Press, vol. 9(03), pages 343-362, June.
    8. Leybourne, S J & McCabe, B P M, 1999. "Modified Stationarity Tests with Data-Dependent Model-Selection Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(2), pages 264-270, April.
    9. Donggyu Sul & Peter C. B. Phillips & Chi-Young Choi, 2005. "Prewhitening Bias in HAC Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(4), pages 517-546, August.
    10. Cheung, Yin-Wong & Chinn, Menzie D, 1997. "Further Investigation of the Uncertain Unit Root in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 68-73, January.
    11. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    12. Rothman, Philip, 1997. "More Uncertainty about the Unit Root in U.S. Real GNP," Journal of Macroeconomics, Elsevier, vol. 19(4), pages 771-780, October.
    13. Kuo, Biing-Shen & Mikkola, Anne, 1999. "Re-examining long-run purchasing power parity," Journal of International Money and Finance, Elsevier, vol. 18(2), pages 251-266, February.
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    Citations

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    Cited by:

    1. Hadri, Kaddour & Kurozumi, Eiji, 2012. "A simple panel stationarity test in the presence of serial correlation and a common factor," Economics Letters, Elsevier, vol. 115(1), pages 31-34.
    2. Skrobotov Anton, 2013. "Bias Correction of KPSS Test with Structural Break for Reducing of Size Distortion," Journal of Time Series Econometrics, De Gruyter, vol. 6(1), pages 33-61, December.
    3. Anton Skrobotov, 2012. "Bias Correction of KPSS Test with Structural Break for Reducing of Size Distortion - in Russian," Working Papers 0044, Gaidar Institute for Economic Policy, revised 2012.
    4. Kaddour Hadri & Eiji Kurozumi & Daisuke Yamazaki, 2015. "Synergy between an Improved Covariate Unit Root Test and Cross-sectionally Dependent Panel Data Unit Root Tests," Manchester School, University of Manchester, vol. 83(6), pages 676-700, December.
    5. Eiji Kurozumi & Daisuke Yamazaki & Kaddour Hadri, 2012. "Covariate Unit Root Test for Cross-Sectionally Dependent Panel Data," Global COE Hi-Stat Discussion Paper Series gd12-256, Institute of Economic Research, Hitotsubashi University.
    6. Manuel Landajo & María Presno, 2013. "Nonparametric pseudo-Lagrange multiplier stationarity testing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 125-147, February.
    7. Nazlioglu, Saban & Karul, Cagin, 2017. "A panel stationarity test with gradual structural shifts: Re-investigate the international commodity price shocks," Economic Modelling, Elsevier, vol. 61(C), pages 181-192.
    8. Lee, Jin & Lee, Young Im, 2012. "Size improvement of the KPSS test using sieve bootstraps," Economics Letters, Elsevier, vol. 116(3), pages 483-486.
    9. Tang, Chor Foon & Tan, Bee Wah, 2015. "The impact of energy consumption, income and foreign direct investment on carbon dioxide emissions in Vietnam," Energy, Elsevier, vol. 79(C), pages 447-454.

    More about this item

    Keywords

    Stationary test; size distortion; boundary rule; bias correction;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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