Break point estimators for a slope shift: levels versus first differences
Article first published online: 16 FEB 2012
© 2012 The Author(s). The Econometrics Journal © 2012 Royal Economic Society.
The Econometrics Journal
Volume 15, Issue 1, pages 154–169, February 2012
How to Cite
Yang, J. (2012), Break point estimators for a slope shift: levels versus first differences. The Econometrics Journal, 15: 154–169. doi: 10.1111/j.1368-423X.2011.00355.x
- Issue published online: 16 FEB 2012
- Article first published online: 16 FEB 2012
- First version received: March 2010; final version accepted: July 2011
- First difference;
- Limiting distribution;
- Linear process;
- Pitman drift;
- Trend shift
Summary This paper analyses two break point estimators: one for a univariate slope-shift model under unit root errors, the other for its first difference (a mean shift model). The asymptotic theory is developed for the estimators under a specific Pitman drift, assuming the break magnitude is within a T−1/2 neighbourhood of zero. Compared to the existing asymptotics assuming a fixed break magnitude or a shrinking one converging at a slower rate than T1/2, the limiting distributions here closely resemble the finite sample distributions of the break point estimators, especially the tail behaviours. Though with a lower convergence rate, the break point estimator from level model concentrates more around the true break point when the break magnitude is small relative to the noise magnitude. With the new limiting distributions, thresholds are provided for empirical researchers to choose the break point estimator based on a mean squared error criterion.