# A Comparison of Alternative Asymptotic Frameworks to Analyze a Structural Change in a Linear Time Trend

*Ai Deng* () and
*Pierre Perron* ()

No WP2005-030, Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics

**Abstract:**
This paper considers various asymptotic approximations to the finite sample distribution of the estimate of the break date in a simple one-break model for a linear trend function that exhibits a change in slope, with or without a concurrent change in intercept. The noise component is either stationary or has an autoregressive unit root. Our main focus is on comparing the so-called “bounded-trend” and “unbounded-trend” asymptotic frameworks. Not surprisingly, the “bounded-trend” asymptotic framework is of little use when the noise component is integrated. When the noise component is stationary, we obtain the following results. If the intercept does not change and is not allowed to change in the estimation, both frameworks yield the same approximation. However, when the intercept is allowed to change, whether or not it actually changes in the data, the “bounded-trend" asymptotic framework completely misses important features of the finite sample distribution of the estimate of the break date, especially the pronounced bimodality that was uncovered by Perron and Zhu (2005) and shown to be well captured using the “unbounded-trend” asymptotic framework. Simulation experiments confirm our theoretical findings, which expose the drawbacks of using the “bounded-trend” asymptotic framework in the context of structural change models.

**Keywords:** change-point; confidence intervals; shrinking shifts; bounded trend; level shift. (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-ets and nep-mac

**Date:** 2005-08

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

**Related works:**

Journal Article: A comparison of alternative asymptotic frameworks to analyse a structural change in a linear time trend (2006)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:bos:wpaper:wp2005-030

Access Statistics for this paper

More papers in Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics Contact information at EDIRC.

Bibliographic data for series maintained by Program Coordinator ().