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A comparison of alternative asymptotic frameworks to analyse a structural change in a linear time trend

机译：比较替代渐近框架以分析线性时间趋势中的结构变化

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摘要

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.
机译：本文针对线性趋势函数的单次中断模型，考虑了中断日期估计的有限样本分布的各种渐近近似，该线性趋势函数显示出斜率发生变化，截距同时发生或不发生变化。噪声分量是固定的或具有自回归单位根。我们的主要重点是比较所谓的“有界趋势”和“无界趋势”渐近框架。毫不奇怪，当噪声成分被集成时，“边界趋势”渐近框架几乎没有用。当噪声分量稳定时，我们得到以下结果。如果截距不变且估计中不允许更改，则两个框架将得出相同的近似值。但是，当允许截距发生变化时，无论它实际上是否在数据中发生变化，“边界趋势”渐近框架都完全错过了中断日期估算的有限样本分布的重要特征，尤其是明显的双峰性。 Perron和Zhu（2005）发现了这一点，并证明了使用“无界趋势”渐近框架可以很好地捕获它。仿真实验证实了我们的理论发现，这揭示了在结构变化模型的背景下使用“有界趋势”渐近框架的弊端。

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