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Testing the unit root hypothesis using generalized range statistics

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  • GIUSEPPE CAVALIERE

Abstract

The application of rescaled range statistics in econometrics is restricted to long memory detection in economic and financial time series. However, in this paper it is shown how such statistics can be generalized and used to test the unit root hypothesis. The proposed generalizations lead to testing procedures that are found to be consistent against I (0 , I (2 as well as against fractional integration and misspecification of the deterministic trend. A Monte Carlo simulation reveals that range-based tests can even outperform standard approaches to nonstationarity tests.

Suggested Citation

  • Giuseppe Cavaliere, 2001. "Testing the unit root hypothesis using generalized range statistics," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-39.
  • Handle: RePEc:ect:emjrnl:v:4:y:2001:i:1:p:39a
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    References listed on IDEAS

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    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
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    4. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
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    6. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
    7. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
    8. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
    9. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    10. Donald W. K. Andrews & C. John McDermott, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," Review of Economic Studies, Oxford University Press, vol. 62(3), pages 343-360.
    11. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    12. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
    13. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
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    Citations

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    Cited by:

    1. In Choi, 2014. "Unit root tests for dependent and heterogeneous micropanels," Working Papers 1404, Research Institute for Market Economy, Sogang University.
    2. Giuseppe Cavaliere, 2005. "Testing mean reversion in target-zone exchange rates," Applied Economics, Taylor & Francis Journals, vol. 37(20), pages 2335-2347.
    3. Karim M. Abadir & Gabriel Talmain, 2008. "Macro and Financial Markets: The Memory of an Elephant?," Working Paper series 17_08, Rimini Centre for Economic Analysis.
    4. repec:spr:stmapp:v:11:y:2002:i:1:d:10.1007_bf02511445 is not listed on IDEAS
    5. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2009. "Two estimators of the long-run variance: Beyond short memory," Journal of Econometrics, Elsevier, vol. 150(1), pages 56-70, May.
    6. Christopher Krauss & Klaus Herrmann, 2017. "On the Power and Size Properties of Cointegration Tests in the Light of High-Frequency Stylized Facts," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(1), pages 1-24, February.
    7. Abadir, Karim & Talmain, Gabriel, 2005. "Distilling co-movements from persistent macro and financial series," Working Paper Series 525, European Central Bank.
    8. Karim M. Abadir, 2013. "Lies, Damned Lies, and Statistics? Examples From Finance and Economics," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 5(4), pages 231-248, December.
    9. Cunado, J. & Gil-Alana, L. A. & Perez de Gracia, F., 2004. "Real convergence in Taiwan: a fractionally integrated approach," Journal of Asian Economics, Elsevier, vol. 15(3), pages 529-547, June.
    10. Karim M. Abadir & Gabriel Talmain, 2012. "Beyond Co-Integration: Modelling Co-Movements in Macro finance," Working Paper series 25_12, Rimini Centre for Economic Analysis.

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