Extensions and Applications of State-Space Models with Markov-Switching: Hypothesis Testing

马尔可夫切换状态空间模型的扩展和应用：假设检验

• 批准号: 9818789
• 负责人: Charles Nelson
• 金额: $ 7.54万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-04-01 至 2001-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9818789&HistoricalAwards=false
• 关键词: Extensions; Applications; State; Space; Models

The first stage of the overall research program of Nelson and Kim was to develop a classical approach to making inferences of state-space models with Markov-switching and their applications. With the algorithm for approximate maximum likelihood estimation developed by Kim (1994), a broad class of models becomes operational that could not be handled before. The resulting model and the algorithm have been applied by principal investigators to various topics in macroeconomics and finance. (Kim and Nelson (1998), Kim and M. Kim (1996).)The second stage of the program made Bayesian Gibbs sampling operational for the state-space model with Markov switching, building upon ideas in Albert and Chib (1993) and Carter and Kohn (1994). The methods were applied to: modeling business cycle asymmetry and comovement; testing business cycle duration dependence in a multivariate context (Kim and Nelson, 1998); and to modeling long-run U.S./U.K. real exchange rate. (Engel and Kim, 1998).The third stage of the program was devoted to writing a book in order to introduce to a wider audience of researchers in economics and finance recent advances in the estimation of state-space models in which switching between regimes occurs stochastically according to a Markov process. The book, titled State-Space Models with Regime-Switching: Classical and Gibbs-Sampling Approaches with Applications, (Kim and Nelson, 1998), is forthcoming from the MIT Press.While estimation of the models with Markov-switching has been well developed in the literature in both the classical and the Bayesian perspectives and their applications are abundant, there apparently seems to be a lag in the literature in the development of procedures for hypothesis testing. Thus, in this fourth stage of the research program, the investigators are designing various hypothesis tests within Markov-switching models. The current stage of the program consists of three related projects. First, they develop a test for structural change at an unknown changepoint in the hyperparameters of Markov-switching models that are otherwise assumed fixed. As an application, Nelson adn Kim test whether the U.S. economy has become more stable. In the second project, they develop a test of Markov-switching within a univariate framework. In the third project, they further extend the second project to develop a test of Markov-switching within a multivariate framework of a dynamic factor model. Tests of Markov-switching within both univariate and multivariate frameworks are based on the posterior probabilities of the model indicator parameters. The second and third projects test whether asymmetry is an important feature of the business cycle.

纳尔逊和金的总体研究计划的第一阶段是开发一个经典的方法，使马尔可夫转换的状态空间模型的推论及其应用。使用Kim（1994）开发的近似最大似然估计算法，以前无法处理的广泛类别的模型变得可操作。由此产生的模型和算法已被主要研究人员应用于宏观经济学和金融学的各种主题。(Kim和纳尔逊（1998），金和M. Kim（1996）.）该计划的第二阶段使贝叶斯吉布斯抽样可用于具有马尔可夫切换的状态空间模型，建立在Albert和Chib（1993）以及Carter和Kohn（1994）的思想基础上。这些方法适用于：建模商业周期不对称和联动;在多元背景下测试商业周期持续时间依赖性（Kim和纳尔逊，1998年）;以及建模长期美国/英国真实的汇率。（Engel and Kim，1998）第三阶段的工作是编写一本书，向更多的经济学和金融学研究人员介绍状态空间模型的最新进展，在该模型中，根据马尔可夫过程随机发生制度之间的转换。这本书，题为状态空间模型与政权切换：经典和吉布斯抽样方法及其应用，（Kim和纳尔逊，1998），即将由MIT出版社出版。虽然在经典和贝叶斯观点的文献中已经很好地发展了具有马尔可夫转换的模型的估计，并且它们的应用是丰富的，在发展假设检验程序方面，文献显然滞后。因此，在研究计划的第四阶段，研究人员正在马尔可夫转换模型中设计各种假设检验。该方案现阶段包括三个相关项目。首先，他们开发了一个测试的结构变化在一个未知的变点在马尔可夫切换模型的超参数，否则假设固定。作为一个应用，纳尔逊和金测试美国经济是否变得更加稳定。在第二个项目中，他们开发了一个单变量框架内的马尔可夫转换测试。在第三个项目中，他们进一步扩展了第二个项目，在动态因子模型的多变量框架内开发马尔可夫转换测试。单变量和多变量框架内的马尔可夫转换检验基于模型指标参数的后验概率。第二个和第三个项目检验不对称性是否是商业周期的一个重要特征。