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arXiv · 1802.05333

Bootstrap-Assisted Unit Root Testing With Piecewise Locally Stationary Errors

Yeonwoo Rho·Xiaofeng Shao
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Abstract

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 non-pivotal 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. Further, 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.

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Yeonwoo Rho, Xiaofeng Shao. 2018-02-14. Bootstrap-Assisted Unit Root Testing With Piecewise Locally Stationary Errors. https://arxiv.org/abs/1802.05333

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