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On the Robustness of Unit Root Tests in the Presence of Double Unit Roots
Author(s) -
HALDRUP NIELS,
LILDHOLDT PETER
Publication year - 2002
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00260
Subject(s) - unit root , mathematics , explosive material , augmented dickey–fuller test , robustness (evolution) , parametric statistics , unit root test , series (stratigraphy) , infinity , unit (ring theory) , statistics , mathematical analysis , paleontology , biochemistry , chemistry , organic chemistry , cointegration , biology , gene , mathematics education
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.