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

Author

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  • 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
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    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.
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    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.

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    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

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