Bootstrapping in Autoregressions: Threshold Estimation and Inference

9807111 Hansen这个项目在两个不同的领域开发了计量经济学估计和推理的新工具。(1)新的自举置信区间的情况下，t统计量不是近似无干扰参数。作为感兴趣的一个主要例子，具有局部到单位自回归根的AR(1)模型中的t统计量的分布不是渐近关键的。在许多动态和非线性模型中也出现了类似的困难。标准的引导方法在这种上下文中不能正常工作。该项目在感兴趣的参数的网格上计算bootstrap分布，将所有干扰参数固定在样本估计值上。准确的自举置信区间很容易从这样的自举分布中构造出来，并且蒙特卡罗模拟在置信区间覆盖方面显示出重要的增益。将这些技术扩展到处理向量值参数的置信区域构造。扩展到非线性计量经济模型也将考虑。(2)阈值模型。当基于连续分布的协变量将样本分成组时，就会出现阈值。推理的难点在于未知阈值的估计。已知最小二乘估计是超一致的，并且具有非标准渐近分布。提出了最小二乘准则函数的一种新的渐近逼近，并用于构造渐近有效置信区间。将该方法扩展到非动态面板，并将扩展到2SLS估计。阈值自回归模型在时间序列文献中尤其流行。?？

9807111 Hansen This project develops new tools for econometric estimation and inference in two distinct areas of interest. (1) New bootstrap confidence intervals for cases where t-statistics are not approximately free of nuisance parameters. As a leading example of interest, the distribution of the t-statistic in the AR(1) model with a local-to-unity autoregressive root is not asymptotically pivotal. Similar difficulties arise in many dynamic and nonlinear models. Standard bootstrap methods do not work properly in such contexts. The project calculates bootstrap distributions on a grid of the parameter of interest, holding all nuisance parameters fixed at the sample estimates. Accurate bootstrap confidence intervals are easy to construct from such bootstrap distributions and Monte Carlo simulations show important gains in confidence interval coverage. These techniques are extended to handle confidence region construction for vector-valued parameters. Extensions to non-linear econometric models will also be considered. (2) Threshold models. A threshold arises when a sample is split into groups based on a continuously-distributed covariate. The difficulty in inference concerns estimation of the unknown threshold. It is known that the least-squares estimate is super-consistent and has a non-standard asymptotic distribution. A new asymptotic approximation to the least squares criterion function is developed and used to construct asymptotically valid confidence intervals. The methods are extended to non-dynamic panels, and will be extended to 2SLS estimation. Threshold autoregressive models are especially popular in the time series literature. ??