The effect of recursive detrending on panel unit root tests
递归去趋势对面板单位根检验的影响AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究面板单位根检验、非线性趋势与局部功效，直接对应宏观面板和时间序列方法。
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递归去趋势对面板单位根检验的影响
- 研究问题
- 当面板序列具有可能非线性的趋势时，递归去趋势如何影响单位根检验的零假设分布、局部功效与局部备择收缩速率？
- 方法与思路
- 作者先在多项式趋势和独立同分布误差下分析新统计量，再提出不要求趋势为多项式、误差独立同分布的稳健统计量。
- 材料陈述的贡献
- 摘要称，首个统计量的零假设极限不依赖真实趋势及拟合阶数，但局部功效随阶数增加而下降；另提供更一般的稳健检验。
- 阅读关注点
- 应核对递归去趋势的实现、面板维度增长方式、阶数不变性的证明范围，以及稳健统计量允许哪些误差依赖和趋势形式。
- 阅读边界
- 出版社摘要明确首组结果依赖简化假设，但未给稳健检验的完整条件；不能将零假设下的不变性直接推广到局部备择。
原文摘要
This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.