This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive, and derive the limiting distributions of the OLS estimators of the model parameters. This allows inferences to be drawn on the overall persistence of the process (as measured by the sum of the autoregressive coefficients), and for the null of a unit root to be tested in the presence of censoring. Our simulations illustrate that the conventional ADF test substantially over-rejects when the data is generated by a dynamic Tobit with a unit root. We provide an application of our methods to testing for a unit root in the Swiss franc / euro exchange rate, during a period when this was subject to an occasionally binding lower bound.

翻译：本文研究具有高度持久性的时间序列，这类序列常受删失或偶发约束等非线性特征影响（如在宏观经济学中常见）。针对此类序列，本文提出一个易于处理的候选模型——具有局部单位根动态特征的Tobit模型。我们证明，该模型生成的过程弱收敛于受约束（调控）为正的非标准极限过程，并推导了模型参数OLS估计量的极限分布。这使研究者能够推断过程的整体持久性（以自回归系数之和衡量），并在存在删失的情况下检验单位根原假设。数值模拟表明，当数据由动态单位根Tobit模型生成时，传统ADF检验会显著过度拒绝原假设。我们将该方法应用于瑞士法郎/欧元汇率在偶发下限约束期间的单位根检验。