We introduce a generalization of the popular local-to-unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local-to-unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and Yogo's (2006) popular inference method for predictive regressions fails to control size in the GLTU(2) model with empirically plausible parameter values, and we propose a limited-information Bayesian framework for inference in the GLTU(p) model and apply it to quantify the uncertainty about the half-life of deviations from purchasing power parity.

中文翻译：

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广义局部到统一模型

我们通过允许p 个自回归 (AR) 根和p  - 1 个接近统一的移动平均 (MA) 根来介绍流行的时间序列持久性局部到统一模型的泛化。这种广义的局部到统一模型 GLTU( p ) 将适当缩放的时间序列收敛到连续时间高斯 ARMA( p , p − 1) 在单位间隔上处理。我们的主要理论结果确立了这个模型类的丰富性，因为它可以很好地近似一大类具有平稳高斯限制的过程，这些过程与单位根基准并不完全不同。我们表明 Campbell 和 Yogo (2006) 流行的预测回归推理方法无法通过经验上合理的参数值控制 GLTU(2) 模型中的大小，并且我们在 GLTU( p ) 模型中提出了一个信息有限的贝叶斯框架进行推理并将其应用于量化偏离购买力平价的半衰期的不确定性。