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Asymptotic null distributions of stationarity and nonstationarity

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Author Info
Nunzio Cappuccio () (Department of Economics (University of Padova))
Diego Lubian () (Department of Economics (University of Verona))

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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.

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File URL: http://dse.univr.it/RePEc/ver/Wpaper/WP8.pdf
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Publisher Info
Paper provided by Università di Verona, Dipartimento di Scienze economiche in its series Working Papers with number 8.

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Length: 27
Date of creation: Sep 2003
Date of revision:
Handle: RePEc:ver:wpaper:8

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Related research
Keywords: Stable distributions; unit root tests; stationarity tests; asymptotic distributions; local-to-finite variance; size distortion;

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
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    Other versions:
  4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
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  9. 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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  10. Stock, James H., 1994. "Deciding between I(1) and I(0)," Journal of Econometrics, Elsevier, vol. 63(1), pages 105-131, July. [Downloadable!] (restricted)
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  11. repec:cup:etheor:v:13:y:1997:i:4:p:506-28 is not listed on IDEAS
  12. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Blackwell Publishing, vol. 53(3), pages 369-84, July. [Downloadable!] (restricted)
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  14. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September. [Downloadable!] (restricted)
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  15. 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. [Downloadable!] (restricted)
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