Improved Andrews’ formula for testing changing mean

A truncated-bandwidth rule (an improved Andrews’ formula) that restores size control and monotonic power for the classical CUSUM and QS mean-shift tests.

Li, W., Zhang, X. and Zu, Y. (2026). Economics Letters 268, 113141.

Abstract

We propose a robust bandwidth rule for the classical CUSUM and QS tests for shifts in the mean of a time series: the AR(1) coefficient entering Andrews’ (1991) data-driven HAC bandwidth is truncated at a fixed threshold \(p_0<1\), with \(p_0\) selected by a simulation-based procedure that controls empirical size against a user-specified persistence robustness target. The truncated bandwidth is shown to be free from the asymptotic power reversal problem under the diverging-alternatives framework of Juhl and Xiao (2009). Monte Carlo evidence indicates that the CUSUM and QS tests implemented with this bandwidth deliver good size control and monotonic power across a range of break designs and persistence levels.

Links

• Journal
• Code (R) — installable R package for the test and bandwidth calibration

BibTeX

@article{li2026improved,
  title   = {Improved Andrews' formula for testing changing mean},
  author  = {Li, Wei and Zhang, Xinyue and Zu, Yang},
  journal = {Economics Letters},
  volume  = {268},
  pages   = {113141},
  year    = {2026},
  doi     = {10.1016/j.econlet.2026.113141}
}