New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade.

开发了新方法来识别、估计和执行具有接近统一的自回归根的非平稳时间序列的推理。该方法在新模型公式中包含单位根 (UR)、局部单位根 (LUR)、轻度集成 (MI) 和轻度爆炸 (ME) 规范。它显示了如何在所有情况下一致地估计涉及表征偏离统一性的定位速率序列的新参数化。能够对非平稳性的形式和程度进行有效推断的简单关键极限分布适用于 MI 和 ME 规范，新极限理论适用于 UR 和 LUR 情况。探索了新参数化的归一化和方差稳定特性。据报道，模拟揭示了这种非平稳时间序列的替代公式的一些优点。对这些方法进行了住房市场应用，区分了过去十年澳大利亚各州首府城市房价行为的不同形式。