Inference When a Parameter Is Not Identified Under the Null

对结构变化和参数不稳定性的测试具有长期的 计量经济学和统计学史。参数经常 减少形式的不可观察的，如品味，技术和 机构职能体系尽管有理由相信， 不可观测量在采样周期内大致恒定， 它很少是先验明显的，因此应该受到 规格测试尽管对这一问题的研究历史悠久 问题，大多数研究人员采用简单的样本分裂测试或 预测误差测试，两者都不是最佳的。的目的 本项目旨在开发一个功能强大的参数测试 在常数零假设下计算的不稳定性 这些参数即使在非线性环境中也易于计算。 所采用的方法是使用近似的拉格朗日乘子 检验参数是否为鞅。这 包括简单的结构突变和随机游动。的 渐近分布是非标准的，但对干扰不变 参数，如果回归量是非趋势的。适当 渐近理论的发展，这使得利用一些最近的 随机过程理论的发展。

Testing for structural change and parameter instability has a long history in econometrics and statistics. Parameters are frequently reduced forms of unobservables, such as taste, technology and institutions. Although it may be reasonable to believe that these unobservables have been roughly constant over the sample period, it is rarely a priori obvious and should therefore be subject to a specification test. Despite the long history of study of this problem, most researchers apply simple sample split tests or forecast error tests, neither of which are optimal. The purpose of this project is to develop a powerful test for parameter instability calculated under the null hypothesis of constant parameters which is easy to calculate, even in non-linear contexts. The approach taken is to use an approximate Lagrange Multiplier test against the alternative that the parameter is martingale. This includes simple structural breaks as well as random walks. The asymptotic distribution is non-standard, but invariant to nuisance parameters if the regressors are non-trended. Appropriate asymptotic theory is developed, which makes use of some recent developments in stochastic process theory.