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Asymptotic null distributions of stationarity and nonstationarity

Author

Listed:
  • Nunzio Cappuccio

    (Department of Economics (University of Padova))

  • Diego Lubian

    (Department of Economics (University of Verona))

Abstract
The purpose of this paper is to investigate the asymptotic null distribution of stationarity and nonstationarity tests when the distribution of the error term belongs to the normal domain of attraction of a stable law in any finite sample but the error term is an i.i.d. process with finite variance as T " 1. This local-to-finite variance setup is helpful to highlight the behavior of test statistics under the null hypothesis in the borderline or near borderline cases between finite and infinite variance and to assess the robustness of these test statistics to small departures from the standard finite variance context. From an empirical point of view, our analysis can be useful in settings where the (non)-existence of the (second) moments is not clear-cut, such as, for example, in the analysis of financial time series. A Monte Carlo simulation study is performed to improve our understanding of the practical implications of the limi theory we develop. The main purpose of the simulation experiment is to assess the size distortion of the unit root and stationarity tests under investigation.

Suggested Citation

  • Nunzio Cappuccio & Diego Lubian, 2003. "Asymptotic null distributions of stationarity and nonstationarity," Working Papers 08/2003, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:08/2003
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    File URL: http://dse.univr.it/RePEc/ver/Wpaper/WP8.pdf
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    References listed on IDEAS

    as
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    5. Phillips, P.C.B., 1990. "Time Series Regression With a Unit Root and Infinite-Variance Errors," Econometric Theory, Cambridge University Press, vol. 6(1), pages 44-62, March.
    6. 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.
    7. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
    8. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
    9. Zhijie Xiao, 2001. "Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 87-105, January.
    10. Sung Ahn & Stergios Fotopoulos & Lijian He, 2001. "Unit Root Tests With Infinite Variance Errors," Econometric Reviews, Taylor & Francis Journals, vol. 20(4), pages 461-483.
    11. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
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    Cited by:

    1. 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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    More about this item

    Keywords

    Stable distributions; unit root tests; stationarity tests; asymptotic distributions; local-to-finite variance; size distortion;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: 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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