标题： 平稳/非平稳自回归时变参数模型中的推断 显示英文标题

标题： Inference in a Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model

摘要： 本文考虑了一阶自回归（AR(1））模型中非参数估计和推断，该模型具有确定性时间变化的参数。 所提出方法的一个关键特点是允许在某些时间段内存在时间变化的平稳性，在其他时间段内存在时间变化的非平稳性（即单位根或局部单位根行为），并在两者之间存在平滑过渡。 在任何时间点的AR参数估计基于局部最小二乘回归方法，其中相关的初始条件是内生的。 当参数在时间$\tau$展现出单位根、局部单位根或平稳/类似平稳行为时，我们得到了AR参数估计量和t统计量在该点的极限分布，此时参数在时间$\tau$表现出单位根、局部单位根或平稳/类似平稳行为。 这些结果用于构建任意指定时间点的AR参数的置信区间和中位数无偏区间估计量。 置信区间具有正确的渐近覆盖概率，且覆盖概率在观测值的平稳和非平稳行为中保持一致。 显示英文摘要

摘要： This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in some time periods, time-varying nonstationarity (i.e., unit root or local-to-unit root behavior) in other periods, and smooth transitions between the two. The estimation of the AR parameter at any time point is based on a local least squares regression method, where the relevant initial condition is endogenous. We obtain limit distributions for the AR parameter estimator and t-statistic at a given point $\tau$ in time when the parameter exhibits unit root, local-to-unity, or stationary/stationary-like behavior at time $\tau$. These results are used to construct confidence intervals and median-unbiased interval estimators for the AR parameter at any specified point in time. The confidence intervals have correct asymptotic coverage probabilities with the coverage holding uniformly over stationary and nonstationary behavior of the observations.