IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v122y2014i1p64-68.html
   My bibliography  Save this article

Asymptotic behaviour of tests for a unit root against an explosive alternative

Author

Listed:
  • Harvey, David I.
  • Leybourne, Stephen J.

Abstract

We compare the asymptotic local power of upper-tail unit root tests against an explosive alternative based on ordinary least squares (OLS) and quasi-differenced (QD) demeaning/detrending. We find that under an asymptotically negligible initialisation, the QD-based tests are near asymptotically efficient and generally offer superior power to OLS-based approaches; however, the power gains are much more modest than in the lower-tail testing context. We also find that asymptotically non-negligible initial conditions do not affect the power ranking in the same way as they do for lower-tail tests, with the QD-based tests retaining a power advantage in such cases.

Suggested Citation

  • Harvey, David I. & Leybourne, Stephen J., 2014. "Asymptotic behaviour of tests for a unit root against an explosive alternative," Economics Letters, Elsevier, vol. 122(1), pages 64-68.
    • Handle: RePEc:eee:ecolet:v:122:y:2014:i:1:p:64-68
    DOI: 10.1016/j.econlet.2013.11.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016517651300493X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2013.11.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    2. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    3. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    4. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Sinelnikova-Muryleva, Elena & Skrobotov, Anton, 2017. "Testing time series for the bubbles (with application to Russian data)," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 46, pages 90-103.
    2. Kruse, Robinson & Kaufmann, Hendrik & Wegener, Christoph, 2018. "Bias-corrected estimation for speculative bubbles in stock prices," Economic Modelling, Elsevier, vol. 73(C), pages 354-364.
    3. Patrick Marsh, 2019. "Properties of the power envelope for tests against both stationary and explosive alternatives: the effect of trends," Discussion Papers 19/03, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    5. Anton Skrobotov, 2013. "Double Unit Roots Testing, GLS-detrending and Uncertainty over the Initial Conditions," Working Papers 0083, Gaidar Institute for Economic Policy, revised 2013.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Smeekes, Stephan & Taylor, A.M. Robert, 2012. "Bootstrap Union Tests For Unit Roots In The Presence Of Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 28(2), pages 422-456, April.
    2. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, September.
    3. Pierre Perron & Gabriel Rodríguez, "undated". "Residuals-based Tests for Cointegration with GLS Detrended Data," Boston University - Department of Economics - Working Papers Series wp2015-017, Boston University - Department of Economics, revised 19 Oct 2015.
    4. Christoph Hanck, 2012. "Multiple unit root tests under uncertainty over the initial condition: some powerful modifications," Statistical Papers, Springer, vol. 53(3), pages 767-774, August.
    5. Skrobotov Anton, 2018. "On Trend Breaks and Initial Condition in Unit Root Testing," Journal of Time Series Econometrics, De Gruyter, vol. 10(1), pages 1-15, January.
    6. Anna Bykhovskaya & Vadim Gorin, 2020. "Cointegration in large VARs," Papers 2006.14179, arXiv.org, revised Dec 2021.
    7. Aristidou Chrystalleni & Harvey David I. & Leybourne Stephen J., 2017. "The Impact of the Initial Condition on Covariate Augmented Unit Root Tests," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-23, January.
    8. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    9. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    10. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2011. "Testing for Unit Roots and the Impact of Quadratic Trends, with an Application to Relative Primary Commodity Prices," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 514-547, October.
    11. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2010. "The impact of the initial condition on robust tests for a linear trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 292-302, July.
    12. David I. Harvey & Stephen J. Leybourne & Yang Zu, 2019. "Testing explosive bubbles with time-varying volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1131-1151, November.
    13. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
    14. Samuel Brien & Michael Jansson & Morten Ørregaard Nielsen, 2022. "Nearly Efficient Likelihood Ratio Tests of a Unit Root in an Autoregressive Model of Arbitrary Order," Working Paper 1429, Economics Department, Queen's University.
    15. Meng, Ming & Lee, Hyejin & Cho, Myeong Hyeon & Lee, Junsoo, 2013. "Impacts of the initial observation on unit root tests using recursive demeaning and detrending procedures," Economics Letters, Elsevier, vol. 120(2), pages 195-199.
    16. Jansson Michael & Nielsen Morten Ørregaard, 2011. "Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-21, February.
    17. Niklas Ahlgren & Mikael Juselius, 2012. "Tests for cointegration rank and the initial condition," Empirical Economics, Springer, vol. 42(3), pages 667-691, June.
    18. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    19. Martin C. Arnold & Christoph Hanck, 2019. "On Combining Evidence from Heteroskedasticity Robust Panel Unit Root Tests in Pooled Regressions," JRFM, MDPI, vol. 12(3), pages 1-22, July.
    20. Paulo M. M. Rodrigues, 2013. "Recursive adjustment, unit root tests and structural breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 62-82, January.

    More about this item

    Keywords

    Unit root testing; Explosive autoregression; Asymptotic power; Initial condition;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    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:eee:ecolet:v:122:y:2014:i:1:p:64-68. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.