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On the Robustness of Unit Root Tests in the Presence of Double Unit Roots

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  • NIELS HALDRUP
  • PETER LILDHOLDT

Abstract

We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two rather than of order one. It turns out that standard augmented Dickey–Fuller type of tests for a single unit root have excessive density in the explosive region of the distribution. The lower (stationary) tail, however, will be virtually unaffected in the presence of double unit roots. On the other hand, the Phillips–Perron class of semi‐parametric tests is shown to diverge to plus infinity asymptotically and thus favouring the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples.

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  • Niels Haldrup & Peter Lildholdt, 2002. "On the Robustness of Unit Root Tests in the Presence of Double Unit Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(2), pages 155-171, March.
    • Handle: RePEc:bla:jtsera:v:23:y:2002:i:2:p:155-171
    DOI: 10.1111/1467-9892.00260
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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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