REML in time series models: Applications to unified inference in moderate and near integrated autoregressions, dynamic panels, cointegrated systems and non-linear IV regressions

所提出的研究演示了如何限制似然方法可以解决几个众所周知的估计和推理问题。针对具有确定性成分的准整过程的推断问题，本文提出了一个基于卡方分布的具有确定性成分的自回归过程的统一推断框架，无论其是平稳过程、中等整过程、准整过程还是整过程。本文对多元时间序列模型提出了一种加权最小二乘近似约束似然估计方法，使之成为一种计算简单、理论性能优良的方法。该方法还包括将约束似然方法应用于动态面板数据模型中的随机参数问题。还计划进行研究，探讨似乎没有任何结果的非线性模型的有限可能性。这项研究将有助于在统计学和经济学之间架起一座桥梁。 限制似然法已经存在了近四十年，并且经常用于线性混合模型。虽然限制似然在历史上被用于减少偏差，但最近的研究也表明，基于限制似然的似然比检验统计量在非参数模型中具有良好的特性。然而，这大量的工作在很大程度上忽略了其在时间序列模型中的潜在用途，只有极少数例外，包括PI在以前的资助下的研究。这一提议是与统计学研究人员和从业人员以及计量经济学家就有限可能性的应用进行的持续对话。一些项目的目的是促进应用限制的可能性在最广泛使用的计量经济模型。

The proposed research demonstrates how the restricted likelihood approach can resolve several well known estimation and inference problems. For the inference problem of a near integrated process with deterministic components, this research provides a framework for unified inference based on the chi-squared distribution for autoregressive processes with deterministic components regardless of whether they are stationary, moderate integrated, near integrated or integrated processes. A weighted least squares approximate restricted likelihood is provided for multivariate time series models so that a computationally simple method with attractive theoretical properties is available. The proposal also includes using the restricted likelihood for the incidental parameter problem in dynamic panel data model. Research is also planned to explore the restricted likelihood for non-linear models for which there do not seem to be any results available. This research will help to build a bridge between statistics and economics. Restricted likelihood has existed for almost four decades and been routinely used in linear mixed models. While the restricted likelihood has historically been used for bias reduction, recent research has also shown that the restricted likelihood based likelihood ratio test statistic has nice properties in nonparametric models. However, this large body of work on the restricted likelihood has largely ignored its potential use in time series models with only very few exceptions including the PI's research under the previous grant. This proposal is a continuing dialogue with researchers and practitioners in statistics as well as econometricians on the applications of restricted likelihood. A number of projects are presented with the aim of facilitating the application of restricted likelihood in the most widely used econometric models.