贝叶斯框架下半参数门限模型的估计、检验及其应用

The regime probability function of traditional threshold models is an indicator function of the threshold variable. Due to its simplicity and strong explanatory power, traditional threshold models have been widely applied to nonlinear modeling analysis. However, under the setting of the special regime probability function, traditional threshold models cannot effectively capture the complex economic issues, such as changeable threshold values or threshold variables with measurement error. Without changing the basic form of traditional threshold models, this project introduces the threshold variable into the regime probability function in a nonparametric way by employing truncated power polynomial splines, proposes a new class of semiparametric threshold models, and further investigates the issues of estimation, testing and applications under the Bayesian framework. We will conduct the following research: (1) propose Bayesian estimation method for the two-regime semiparametric threshold model and make Bayesian inference; (2) propose Bayesian test method for threshold effect and the form of the regime probability function for the two-regime semiparametric threshold model; (3) extend the above estimation and testing approaches to multi-regime semiparametric threshold models; (4) study the practical value of the above theoretical research achievements in characterizing the regime switching behaviors of stock returns forecasting, monetary policy rule as well as the main macroeconomic variables. The project will enrich the research achievements of threshold models, which is helpful to promote the development of nonlinear modeling.

传统门限模型的区制概率函数是关于门限变量的示性函数，具有估计方法简单及经济解释直观的优点，被广泛地应用于非线性建模分析，但其过于特殊的区制概率函数无法准确刻画门限值可变或者门限变量具有测量误差等复杂经济问题。本课题在保留传统门限模型基本形式不变的同时，借助截尾多项式样条函数，尝试将门限变量以非参数的形式引入区制概率函数，提出一类半参数门限模型，并进一步在贝叶斯框架下探讨其估计、检验及其应用等相关问题。具体研究内容包括：①针对两区制半参数门限模型，提出相应贝叶斯估计方法并进行统计推断；②针对两区制半参数门限模型，提出门限效应和区制概率函数形式的贝叶斯检验方法；③将上述模型的估计和检验方法扩展到多区制半参数门限模型；④探讨上述理论研究成果在刻画我国股票收益率预测、货币政策规则以及主要宏观经济变量的区制转换行为方面的应用价值。本课题丰富了门限模型的研究成果，有助于推动非线性建模领域的发展。

传统门限模型的区制概率函数是关于门限变量的示性函数，具有估计方法简单及经济解释直观的优点，被广泛地应用于非线性建模分析，但其过于特殊的区制概率函数无法准确刻画可变门限值或者门限变量具有测量误差等复杂经济问题。本项目在保留传统门限模型基本形式不变的同时，借助截尾多项式样条函数，将门限变量以非参数的形式引入区制概率函数，提出了一类半参数门限模型，并在贝叶斯框架下对其估计、检验及其应用进行了深入研究。具体研究内容包括：①针对两区制半参数门限模型，提出了相应贝叶斯估计方法并进行统计推断，有效解决了未知参数维数偏高、区制识别约束和平滑性约束等问题；②针对两区制半参数门限模型，提出了一类门限效应的贝叶斯检验方法，为研究人员是否应该使用门限模型提供了严格的理论依据；③探讨了上述理论研究成果在刻画我国股票收益率预测、货币政策规则以及可能存在非线性特征的其他经济金融变量的区制转换行为方面的应用价值，为相关机构制定和评价国家政策提供了新的经验证据。本项目丰富了门限模型的研究成果，有助于推动非线性建模领域的发展。