IDEAS home Printed from https://ideas.repec.org/a/ren/journl/v2y2010i2p169-193.html
   My bibliography  Save this article

Size Distortion of Bootstrap Tests: an Example from Unit Root Testing

Author

Listed:
  • Russell Davidson

    (McGill University, CIREQ, and GREQAM)

Abstract

Testing for a unit root in a series obtained by summing a stationary MA(1) process with a parameter close to -1 leads to serious size distortions under the null, on account of the near cancellation of the unit root by the MA component in the driving stationary series. The situation is analysed from the point of view of bootstrap testing, and an exact quanti- tative account is given of the error in rejection probability of a bootstrap test. A particular method of estimating the MA parameter is recommended, as it leads to very little distortion even when the MA parameter is close to -1. A new bootstrap procedure with still better properties is proposed. While more computationally demanding than the usual bootstrap, it is much less so than the double bootstrap.

Suggested Citation

  • Russell Davidson, 2010. "Size Distortion of Bootstrap Tests: an Example from Unit Root Testing," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 2(2), pages 169-193, June.
    • Handle: RePEc:ren:journl:v:2:y:2010:i:2:p:169-193
    as

    Download full text from publisher

    File URL: http://www.rofea.org/index.php?journal=journal&page=article&op=download&path%5B%5D=36&path%5B%5D=48
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    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. Davidson, Russell, 2017. "A discrete model for bootstrap iteration," Journal of Econometrics, Elsevier, vol. 201(2), pages 228-236.
    2. Kung-Sik Chan & Simone Giannerini & Greta Goracci & Howell Tong, 2020. "Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis," Papers 2002.09968, arXiv.org, revised Nov 2021.

    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. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    2. Erciulescu Andreea L. & Fuller Wayne A., 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Statistics Poland, vol. 17(1), pages 9-24, March.
    3. Marcus J. Chambers, 2015. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics, MDPI, vol. 3(2), pages 1-21, May.
    4. Davidson, Russell & Trokić, Mirza, 2020. "The fast iterated bootstrap," Journal of Econometrics, Elsevier, vol. 218(2), pages 451-475.
    5. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
    6. Bodart, Vincent & Candelon, Bertrand & Carpantier, Jean-Francois, 2015. "Real exchanges rates, commodity prices and structural factors in developing countries," Journal of International Money and Finance, Elsevier, vol. 51(C), pages 264-284.
    7. Chiu, Sung Nok & Wang, Ling, 2009. "Homogeneity tests for several Poisson populations," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4266-4278, October.
    8. Ren, Tongxian & Long, Zhihe & Zhang, Rengui & Chen, Qingqing, 2014. "Moran's I test of spatial panel data model — Based on bootstrap method," Economic Modelling, Elsevier, vol. 41(C), pages 9-14.
    9. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    10. Imran H. Shah & Ian Corrick & Abdul Saboor, 2018. "How should Central Banks Respond to Non-neutral Inflation Expectations?," Open Economies Review, Springer, vol. 29(2), pages 321-351, April.
    11. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Other publications TiSEM d8c37ad3-f9a5-4824-986d-2, Tilburg University, School of Economics and Management.
    12. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    13. Lavergne, Pascal & Bertail, Patrice, 2020. "Bootstrapping Quasi Likelihood Ratio Tests under Misspecification," TSE Working Papers 20-1102, Toulouse School of Economics (TSE).
    14. Davidson, Russell, 2017. "A discrete model for bootstrap iteration," Journal of Econometrics, Elsevier, vol. 201(2), pages 228-236.
    15. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    16. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    17. Jean-Pierre Florens & Elia Lapenta, 2022. "Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments," Papers 2212.11012, arXiv.org, revised Oct 2023.
    18. repec:ipg:wpaper:2014-046 is not listed on IDEAS
    19. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2013. "On the Determinants of Distribution Dynamics," Discussion Papers 2013/165, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    20. Patrick Richard, 2007. "ARMA Sieve bootstrap unit root tests," Cahiers de recherche 07-05, Departement d'économique de l'École de gestion à l'Université de Sherbrooke, revised Jul 2009.
    21. Bolduc, Denis & Khalaf, Lynda & Moyneur, Érick, 2008. "Identification-robust simulation-based inference in joint discrete/continuous models for energy markets," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3148-3161, February.
    22. Lapenta, Elia & Lavergne, Pascal, 2022. "Encompassing Tests for Nonparametric Regressions," TSE Working Papers 22-1332, Toulouse School of Economics (TSE).

    More about this item

    Keywords

    Bootstrap test; unit root; MA(1); size distortion;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:ren:journl:v:2:y:2010:i:2:p:169-193. 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: Dr. Jerzy (Jurek) Konieczny (email available below). General contact details of provider: http://www.rcfea.org/ .

    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.