GLS-BASED UNIT ROOT TESTS WITH MULTIPLE STRUCTURAL BREAKS UNDER BOTH THE NULL AND THE ALTERNATIVE HYPOTHESES
原假设与备择假设下均允许多重结构断点的 GLS 单位根检验AI 解读 ↓
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原假设与备择假设下均允许多重结构断点的 GLS 单位根检验
- 研究问题
- 如何在单位根原假设和趋势平稳备择下都容许多个未知断点，同时改进检验的去趋势方式和局部渐近功效？
- 方法与思路
- 作者扩展未知断点检验框架，容许趋势水平和斜率多次变化，采用准广义最小二乘去趋势，并考虑包括 M 检验的多类统计量。
- 材料陈述的贡献
- 摘要称，扩展覆盖任意数量的水平与斜率变化，并采用可使局部渐近功效接近高斯功效包络的去趋势方法。
- 阅读关注点
- 应核对断点数量、间距和幅度的限制，未知日期的处理，以及已知断点极限分布和接近功效包络结论的适用范围。
- 阅读边界
- 仅据所给 Crossref 摘要，断点数是否已知、增长规则和有限样本表现未说明，不能把任意数量理解为毫无限制。
原文摘要
Perron (1989, Econometrica 57, 1361–1401) introduced unit root tests valid when a break at a known date in the trend function of a time series is present. In particular, they allow a break under both the null and alternative hypotheses and are invariant to the magnitude of the shift in level and/or slope. The subsequent literature devised procedures valid in the case of an unknown break date. However, in doing so most research, in particular the commonly used test of Zivot and Andrews (1992, Journal of Business & Economic Statistics 10, 251–270), assumed that if a break occurs it does so only under the alternative hypothesis of stationarity. This is undesirable for several reasons. Kim and Perron (2009, Journal of Econometrics 148, 1–13) developed a methodology that allows a break at an unknown time under both the null and alternative hypotheses. When a break is present, the limit distribution of the test is the same as in the case of a known break date, allowing increased power while maintaining the correct size. We extend their work in several directions: (1) we allow for an arbitrary number of changes in both the level and slope of the trend function; (2) we adopt the quasi–generalized least squares detrending method advocated by Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836) that permits tests that have local asymptotic power functions close to the local asymptotic Gaussian power envelope; (3) we consider a variety of tests, in particular the class of M -tests introduced in Stock (1999, Cointegration, Causality, and Forecasting: A Festschrift for Clive W.J. Granger ) and analyzed in Ng and Perron (2001, Econometrica 69, 1519–1554).