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

时间序列模型中的 REML：在中等和近积分自回归、动态面板、协整系统和非线性 IV 回归中统一推理的应用

• 批准号: 1007652
• 负责人: Willa Chen
• 金额: $ 14.3万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-05-15 至 2014-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007652&HistoricalAwards=false
• 关键词: REML; time; series; models; Applications

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.

提出的研究证明了限制似然方法如何解决几个众所周知的估计和推理问题。对于具有确定性分量的近积分过程的推理问题，本文提供了一个基于卡方分布的自回归过程统一推理框架，无论该自回归过程是平稳的、中度积分的、近积分的还是积分的。对多变量时间序列模型提出了加权最小二乘近似限制似然，从而提供了一种计算简单、理论性质吸引人的方法。该方法还包括对动态面板数据模型中的附带参数问题使用限制似然方法。研究还计划探索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。有限似然已经存在了近四十年，并经常用于线性混合模型。虽然限制似然历来被用于减少偏差，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性能。然而，这些关于有限似然的大量工作在很大程度上忽略了它在时间序列模型中的潜在用途，只有极少数例外，包括PI在之前的资助下的研究。这一建议是与统计研究人员和实践者以及计量经济学家就限制似然的应用进行的持续对话。提出了一些项目，目的是促进限制似然在最广泛使用的计量经济模型中的应用。