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Local Asymptotic Distributions of Stationarity Tests

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  • Nunzio Cappuccio
  • Diego Lubian

Abstract

. In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non‐stationary process in any finite sample which converges to a stationary process as T ↑ ∞. From the asymptotic distributions, we find that the stationarity tests have non‐trivial power under the above sequence of local alternatives. Our results complement those of Wright [Econometric Theory (1999) Vol. 15, pp. 704–709] who found that the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and the modified range statistics (MRS) tests have power equal to their size under a sequence of fractional alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples.

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  • Nunzio Cappuccio & Diego Lubian, 2006. "Local Asymptotic Distributions of Stationarity Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 323-345, May.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:3:p:323-345
    DOI: 10.1111/j.1467-9892.2005.00471.x
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    Cited by:

    1. Wagner, Martin & Wied, Dominik, 2014. "Monitoring Stationarity and Cointegration," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100386, Verein für Socialpolitik / German Economic Association.
    2. Nunzio Cappuccio & Diego Lubian, 2010. "The fragility of the KPSS stationarity test," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 237-253, June.
    3. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.

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