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Testing Stationarity in Small‐ and Medium‐Sized Samples when Disturbances are Serially Correlated

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  • Kristian Jönsson

Abstract

In this paper, we study the size distortions of the KPSS test for stationarity when serial correlation is present and samples are small and medium-sized. It is argued that two distinct sources of the size distortions can be identified. The first source is the finite-sample distribution of the long-run variance estimator used in the KPSS test, while the second source of the size distortions is the serial correlation not captured by the long-run variance estimator due to a too narrow choice of truncation lag parameter. When the relative importance of the two sources is studied, it is found that the size of the KPSS test can be reasonably well controlled if the finite-sample distribution of the KPSS test statistic, conditional on the time-series dimension and the truncation lag parameter, is used. Hence, finite-sample critical values, that can be applied in order to reduce the size distortions of the KPSS test, are supplied. When the power of the test is studied, it is found that the price paid for the increased size control is a lower raw power against a non-stationary alternative hypothesis.
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Suggested Citation

  • Kristian Jönsson, 2011. "Testing Stationarity in Small‐ and Medium‐Sized Samples when Disturbances are Serially Correlated," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 669-690, October.
  • Handle: RePEc:bla:obuest:v:73:y:2011:i:5:p:669-690
    DOI: j.1468-0084.2010.00620.x
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    File URL: http://hdl.handle.net/10.1111/j.1468-0084.2010.00620.x
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    Cited by:

    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. Jönsson, Kristian, 2006. "Finite-Sample Stability of the KPSS Test," Working Papers 2006:23, Lund University, Department of Economics.
    3. 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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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