Bootstrap validity of OLS/2SLS sequential tests with autocorrelated errors

Prove that residual resampling via the moving block bootstrap yields asymptotically valid critical values for OLS and 2SLS sequential sup-F change-point tests in linear time series regressions with autocorrelated errors and multiple change-points.

Background

Errors in local projection regressions are typically autocorrelated, making existing wild-bootstrap validity results (which assume martingale difference errors) inapplicable for sequential multiple-break testing. The authors point out a gap and conjecture that a moving block bootstrap could address autocorrelation while preserving validity of the sequential testing framework.