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The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test

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  • Burridge, Peter
  • Guerre, Emmanuel

Abstract

We derive the limit distribution of the number of crossings of a level by a random walk with continuously distributed increments, using a Brownian motion local time approximation. This complements the well-known result for the random walk on the integers. Use of the frequency of level crossings to test for a unit root is examined.

Suggested Citation

  • Burridge, Peter & Guerre, Emmanuel, 1996. "The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test," Econometric Theory, Cambridge University Press, vol. 12(04), pages 705-723, October.
  • Handle: RePEc:cup:etheor:v:12:y:1996:i:04:p:705-723_00
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    Cited by:

    1. García, Ana & Aparicio, Felipe M. & Escribano, Álvaro, 2004. "A range unit root test," DES - Working Papers. Statistics and Econometrics. WS ws041104, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. So, Beong Soo & Shin, Dong Wan, 2001. "An invariant sign test for random walks based on recursive median adjustment," Journal of Econometrics, Elsevier, vol. 102(2), pages 197-229, June.
    3. In Choi, 2014. "Unit root tests for dependent and heterogeneous micropanels," Working Papers 1404, Research Institute for Market Economy, Sogang University.
    4. Kramer, Walter & Davies, Laurie, 2002. "Testing for unit roots in the context of misspecified logarithmic random walks," Economics Letters, Elsevier, vol. 74(3), pages 313-319, February.
    5. Ivan Paya & Agustin Duarte & Ken Holden, 2007. "On the Relationship between Inflation Persistence and Temporal Aggregation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1521-1531, September.
    6. Shin, Dong Wan & So, Beong Soo, 2000. "Gaussian tests for seasonal unit roots based on Cauchy estimation and recursive mean adjustments," Journal of Econometrics, Elsevier, vol. 99(1), pages 107-137, November.
    7. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
    8. Dias, Daniel A. & Marques, Carlos Robalo, 2010. "Using mean reversion as a measure of persistence," Economic Modelling, Elsevier, vol. 27(1), pages 262-273, January.
    9. Aparicio, Felipe M., 2003. "On the record properties of integrated time series," DES - Working Papers. Statistics and Econometrics. WS ws036414, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Park, Soo Jung & Shin, Dong Wan, 2006. "A sign test for unit roots in a momentum threshold autoregressive process," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 986-990, May.
    11. repec:lan:wpaper:2606 is not listed on IDEAS
    12. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    13. repec:lan:wpaper:2464 is not listed on IDEAS
    14. García, Ana & Aparicio, Felipe M. & Escribano, Álvaro, 2003. "Range unit root tests," DES - Working Papers. Statistics and Econometrics. WS ws031126, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Kunst, Robert M., 2014. "A Combined Nonparametric Test for Seasonal Unit Roots," Economics Series 303, Institute for Advanced Studies.
    16. Kunst, Robert M., 2009. "A Nonparametric Test for Seasonal Unit Roots," Economics Series 233, Institute for Advanced Studies.

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