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  • Yeonwoo Rho (a1) and Xiaofeng Shao (a2)

In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to approximate the nonpivotal limiting null distributions and provide a rigorous theoretical justification for bootstrap consistency. The proposed method is compared through finite sample simulations with the recolored wild bootstrap procedure, which was developed for errors that follow a heteroscedastic linear process. Furthermore, a combination of autoregressive sieve recoloring with the dependent wild bootstrap is shown to perform well. The validity of the dependent wild bootstrap in a nonstationary setting is demonstrated for the first time, showing the possibility of extensions to other inference problems associated with locally stationary processes.

Corresponding author
*Address correspondence to Yeonwoo Rho, Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA; e-mail:
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This research was partially supported by NSF grant DMS-1104545. We are grateful to the co-editor and the three referees for their constructive comments and suggestions that led to a substantial improvement of the article. In particular, we are most grateful to Peter C.B. Phillips, who has gone beyond the call of duty for an editor in carefully correcting our English. We also thank Fabrizio Zanello, Mark Gockenbach, Benjamin Ong, and Meghan Campbell for proofreading. Superior, a high performance computing cluster at Michigan Technological University, was used in obtaining results presented in this publication.

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Econometric Theory
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