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

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Author Info
Ai Deng () (Department of Economics, Boston University)
Pierre Perron () (Columbia Business School)

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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.

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Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2005-030.

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Length: 31 pages
Date of creation: Aug 2005
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Handle: RePEc:bos:wpaper:wp2005-030

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Keywords: change-point confidence intervals shrinking shifts bounded trend level shift.

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