高维近似因子模型的极大似然分析：理论与方法

项目名称： 高维近似因子模型的极大似然分析：理论与方法

项目编号： No.71201031

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 管理科学与工程

项目作者： 李鲲鹏

作者单位： 首都经济贸易大学

项目金额： 21万元

中文摘要： 高维近似因子模型在经济学、金融学、社会学、心理学领域有着广阔的应用空间。在美国，高维近似因子模型是美联储进行货币政策分析的主要工具。但是，关于这一模型的渐近理论，我们却知道的很有限。传统的因子模型估计方法有两种，主成分方法和极大似然方法。从文献角度上看，现有的理论研究基本上都局限于主成分方法。主成分方法有着计算方便简单的优点，但是缺点也很突出。首先，它不能解决受约束因子模型；其次，在估计过程中效率损失也比较大。与之相比，极大似然方法适用范围更广、效率更高。尽管极大似然估计有着各种令人满意的性质，但是这一估计方法的分析框架却迟迟没有建立起来，至今仍然是一个世界性的理论空白。本研究的目标就是为高维近似因子模型的极大似然分析建立其分析框架，填补这一理论空白，同时使现有文献关于高维因子分析的理论框架更为完整。本研究在中国的经济、金融方面亦有广阔的应用空间。

中文关键词： 高维数据；极大似然方法；因子分析；交互效应；ARCH效应

英文摘要： Approximate factor models of high dimension have wide applicability in economics, finance, sociology and psychology. In US, approximate factor models is one of primary tools to evaluate the Fed's monetary policies. Despite the model's wide applicability, the inferential theory for high dimensional factor models is less well understood. From the perspective of history, factor models can be estimated by two methods, that is, the principal components method and maximum likelihood method. However, nearly all the literature on factor models of high dimesion is confined to the principal components methods over last decade.The principal components method has the striking advantage of ease of computation. However, the disadvantages are also notable. First, it can't cover a class of restricted factor models; Second, the efficiency is lost when heterogenuity occurs. Comparatively speaking, the likelihood-based method dominates the principal component method for its wider applicability and higher efficiency. While the likelihood-based analysis has all kinds of satisfactory properties, the framework for the likelihood-based analysis has yet not been established and remains a worldwide theoretical blank. The aim of this research is to establish the framework for the likelihood-based analysis. Purpose of this research is not

英文关键词： high-dimensional data；maximum likelihood method；factor analysis；interactive effects；ARCH effects