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The KPSS Test Using Fixed-b Critical Values: Size and Power in Highly Autocorrelated Time Series

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  • Amsler Christine

    (Michigan State University)

  • Schmidt Peter

    (Michigan State University)

  • Vogelsang Timothy J

    (Michigan State University)

Abstract

In this paper we consider the KPSS test. We derive the asymptotic distribution of the statistic under the null of stationarity and under the unit root alternative under the "fixed-b" assumption that the ratio of the number of lags in the long run variance estimate to the sample size is fixed. Regardless of how the number of lags is actually chosen, the fixed-b asymptotic theory provides a better approximation to the finite sample distribution of the statistic than the traditional KPSS asymptotics. If the series being tested is stationary but has strong positive autocorrelation, the KPSS test has substantial size distortions (overrejections). We show that this problem can be more or less solved by using a larger number of lags than has traditionally been used. Using more lags costs power, but using the fixed-b critical values minimizes the power loss.

Suggested Citation

  • Amsler Christine & Schmidt Peter & Vogelsang Timothy J, 2009. "The KPSS Test Using Fixed-b Critical Values: Size and Power in Highly Autocorrelated Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-44, December.
    • Handle: RePEc:bpj:jtsmet:v:1:y:2009:i:1:n:5
    DOI: 10.2202/1941-1928.1027
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    References listed on IDEAS

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    1. Lee, Junsoo, 1996. "On the power of stationarity tests using optimal bandwidth estimates," Economics Letters, Elsevier, vol. 51(2), pages 131-137, May.
    2. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    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. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    5. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    6. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    7. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-166, April.
    8. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    9. 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.
    10. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
    11. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    12. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    13. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    14. Choi, In, 1994. "Residual-Based Tests for the Null of Stationarity with Applications to U.S. Macroeconomic Time Series," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 720-746, August.
    15. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
    16. Pantula, Sastry G, 1991. "Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 63-71, January.
    17. 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.
    18. GIRAITIS, Liudas & KOKOSZKA, Piotr & LEIPUS, Remigijus & TEYSSIÈRE, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," LIDAM Reprints CORE 1594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    3. Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    4. Amsler Christine & Schmidt Peter, 2012. "A Comparison of the Robustness of Several Tests of Short Memory to Autocorrelated Errors," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 56-66, August.
    5. Badi H. Baltagi & Chihwa Kao & Long Liu, 2017. "Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 85-102, March.
    6. Su, Jen-Je & Amsler, Christine & Schmidt, Peter, 2012. "A note on the size of the KPSS unit root test," Economics Letters, Elsevier, vol. 117(3), pages 697-699.
    7. Manuel Landajo & María José Presno, 2010. "Stationarity testing under nonlinear models. Some asymptotic results," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 392-405, September.

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