Collaborative Research: Topics in Factor Analysis of Large Dimensions

随着时间的推移和信息技术的进步，一个不可避免的结果是可用数据量的增加。以前为处理几个变量而开发的方法不适用于分析数百个变量。这项研究的动机是需要经验工具，可以简洁地综合数据，并以促进经济分析的方式。本研究的重点是因子模型。在因子框架中，在大量序列中具有解释力的成分与对数据没有普遍影响的特质成分区分开来。这种共同特质的分解提供了一种有效的方法，可以将大量数据压缩为可管理的因子数量。目前可用于因子分析的统计结果要么假设时间小，要么假设面板的横截面尺寸小。当数据面板的两个维度都很大时，本研究开发了因子分析工具。我们展示了如何通过主成分方法从数据中一致地估计共同和特殊成分，尽管未观察到，无论数据是否平稳。我们将制定统计标准，从数据中确定未知数量的因素。我们还将开发测试，以确定观测数据中的非平稳性是普通类型还是特殊类型。我们将建立主成分估计量的统计性质。还将考虑估计共同因素的不同方法。宏观经济学和金融经济学中的许多问题都可以在一个因素框架内进行研究。例如，商业周期的特点是大量经济时间序列的共同运动。资产回报已被证明具有一个因素结构，特殊的变化是可多样化的，而系统的变化则不是。诸如全球趋势和全球经济衰退等概念经常被使用。因子框架提供了对这些概念的正式处理。我们的研究结果为大维度的因子分析提供了统计基础，使研究人员能够使用几十年的数百个序列、数千年的资产回报、数百个世纪的国家级序列来估计因素并进行推理。这项研究的结果将使人们能够最大限度地利用现有的资料，而不必主观地选择要分析哪个系列。

An inevitable outcome as we move forward in calendar time and as information technology advances is an increase in the volume of data available. Methods previously developed for handling a few variables are not adequate for analyzing hundreds of variables. This research is motivated by the need for empirical tools that can synthesize the data concisely and in ways that facilitate economic analysis. The focus of this research is on factor models. In a factor framework, components that have explanatory power in a large number of series are distinguished from the idiosyncratic ones that do not have pervasive effects on the data. This common-idiosyncratic decomposition provides an effective way of compressing a large volume of data to a manageablenumber of factors. Statistical results currently available for factor analysis assume either the time or the cross-section dimension of the panel is small. This research develops tools for factor analysis when both dimensions of the data panel are large. We show how the common and idiosyncratic components, although unobserved, can be consistently estimated from the data by the method of principal components whether or not the data are stationary. We will develop statistical criteria for determining the unknown number of factors from the data. We will also develop tests to determine whether non-stationarity in the observed data is of the common or idiosyncratic type. We will establish statistical properties of the principal components estimator. Different methods of estimating the common factors will also be considered.Many issues in macro and financial economics can be studied within a factor framework. For example, business cycles are characterized by the co-movement of a large number of economic time series. Asset returns have been shown to have a factor structure, with idiosyncratic variations being diversifiable, while systematic ones are not. Notions such as global trends and worldwide economic downturns are used frequently. The factor framework provides a formal treatment of these concepts. By providing the statistical foundation for factor analysis of large dimensions, our results enable researchers to use hundreds of series over decades, thousands of asset returns over years, and hundreds of country level series over centuries, to estimate the factors and conduct inference. The results of this research will make it possible to make maximum use of information available without having to choose subjectively which series are to be analyzed.