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A bootstrap procedure in linear regression with nonstationary errors

In the context of linear regression with dependent and nonstationary errors, the classical moving‐block bootstrap (MBB) fails to capture the nonstationarity of the errors. A new bootstrap procedure called the blocking external bootstrap (BEB) is proposed to overcome the problem. The consistency of the BEB in estimating the variance of the least‐squares estimator is studied in the case of α‐mixing and nonstationary sequence of errors. It is shown that the BEB only achieves partial correction if the block size is fixed. Complete consistency is achieved by the BEB when the block size is allowed to go to infinity. We also study the first‐order consistency of the least squares estimator based on the BEB. A simulation study is carried out to assess the performance of the BEB versus the MBB in estimating the variance of the least‐squares estimator. Finally, some open problems are discussed.