This paper proposes a new procedure for estimating the number of structural changes in the persistence of a univariate time series. In contrast to the extant literature that primarily assumes (regime-wise) stationarity, our framework also allows the underlying stochastic process to switch between stationary [I(0)] and unit root [I(1)] regimes. We develop a sequential testing approach based on the simultaneous application of two Wald-type tests for structural change, one of which assumes the process is I(0)-stable under the null hypothesis while the other assumes the stable I(1) model as the null hypothesis. This feature allows the procedure to maintain correct asymptotic size regardless of whether the regimes are I(0) or I(1). We also propose a novel procedure for distinguishing processes with pure level and/or trend shifts from those that are also subject to concurrent shifts in persistence. The large sample properties of the recommended procedures are derived and the relevant asymptotic critical values tabulated. Our Monte Carlo experiments demonstrate that the advocated approach compares favorably relative to the commonly employed approach based on I(0) sequential testing, especially when the data contain an I(1) segment.

中文翻译：

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用于估计持久性结构变化数量的稳健顺序程序

本文提出了一种估计单变量时间序列持久性结构变化数量的新程序。与主要假设（体制方面）平稳性的现有文献相比，我们的框架还允许潜在的随机过程在平稳 [I(0)] 和单位根 [I(1)] 体制之间切换。我们开发了一种基于同时应用两个 Wald 型结构变化检验的顺序检验方法，其中一个假设过程在原假设下是 I(0) 稳定的，而另一个假设稳定 I(1) 模型为零假设。此功能允许程序保持正确的渐近大小，而不管机制是 I(0) 还是 I(1)。我们还提出了一种新的程序，用于区分具有纯水平和/或趋势变化的过程与那些同时受到持久性变化的过程。推导出了推荐程序的大样本特性，并列出了相关的渐近临界值。我们的蒙特卡罗实验表明，与基于 I(0) 顺序测试的常用方法相比，所提倡的方法具有优势，尤其是当数据包含 I(1) 段时。