IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v12y1996i04p705-723_00.html
   My bibliography  Save this article

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

Author

Listed:
  • 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(4), pages 705-723, October.
    • Handle: RePEc:cup:etheor:v:12:y:1996:i:04:p:705-723_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S026646660000699X/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aparicio, Felipe M. & Escribano, Álvaro & García, Ana, 2003. "Range unit root tests," DES - Working Papers. Statistics and Econometrics. WS ws031126, 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. 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.
    4. In Choi, 2014. "Unit root tests for dependent and heterogeneous micropanels," Working Papers 1404, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    5. 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.
    6. 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.
    7. repec:lan:wpaper:2606 is not listed on IDEAS
    8. 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.
    9. 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.
    10. repec:lan:wpaper:2464 is not listed on IDEAS
    11. 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.
    12. 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.
    13. In Choi, 2019. "Unit Root Tests for Dependent Micropanels," The Japanese Economic Review, Japanese Economic Association, vol. 70(2), pages 145-167, June.
    14. Pollock D. S. G., 2013. "Cycles, Syllogisms and Semantics: Examining the Idea of Spurious Cycles," Journal of Time Series Econometrics, De Gruyter, vol. 6(1), pages 81-102, September.
    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.
    17. 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.
    18. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:12:y:1996:i:04:p:705-723_00. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.