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

Author

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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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    3. 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.
    4. 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.
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    6. 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.
    7. 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.

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    Keywords

    KPSS; fixed-b; stationarity test;
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