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

Nelson和Kim整体研究计划的第一阶段是发展一种经典的方法，用马尔可夫开关及其应用对状态空间模型进行推理。通过Kim（1994）开发的近似最大似然估计算法，以前无法处理的大量模型变得可操作。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Nelson （1998)， Kim和M. Kim（1996）。）在Albert和Chib（1993）以及Carter和Kohn（1994）的思想基础上，该计划的第二阶段使贝叶斯吉布斯抽样对具有马尔可夫切换的状态空间模型具有可操作性。应用该方法对经济周期的不对称性和一致性进行建模；在多变量背景下测试商业周期持续时间依赖性（Kim和Nelson， 1998）；并对美国和英国的长期关系进行建模实际汇率。（恩格尔和金，1998）。该计划的第三阶段致力于写一本书，以便向更广泛的经济学和金融学研究人员介绍状态空间模型估计方面的最新进展，在状态空间模型中，根据马尔可夫过程随机发生政权之间的切换。这本书，题为状态空间模型与状态交换：经典和吉布斯采样方法与应用，（Kim和Nelson， 1998年），即将从麻省理工学院出版社。尽管从经典和贝叶斯的角度对马尔可夫转换模型的估计已经有了很好的发展，而且它们的应用也很丰富，但在假设检验程序的发展方面，文献显然存在滞后。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。该计划的当前阶段包括三个相关的项目。首先，他们开发了一种在马尔可夫切换模型的超参数中未知变化点的结构变化测试，否则假设这些模型是固定的。作为一项应用，纳尔逊和金测试了美国经济是否变得更加稳定。在第二个项目中，他们在单变量框架内开发了马尔可夫切换的测试。在第三个项目中，他们进一步扩展了第二个项目，在动态因素模型的多元框架内开发马尔可夫开关的测试。在单变量和多变量框架内的马尔可夫转换测试是基于模型指标参数的后验概率的。第二个和第三个项目检验不对称是否是经济周期的一个重要特征。

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.