Collaborative Research: Topics in Factor Analysis of Large Dimensions

随着我们在日历时间的推进和信息技术的进步，一个不可避免的结果是可用的数据量增加。以前开发的处理几个变量的方法不足以分析数百个变量。这项研究的动机是需要能够以简明的方式综合数据并促进经济分析的实证工具。本研究的重点是因素模型。在因子框架中，在大量序列中具有解释能力的成分与对数据没有普遍影响的特殊成分是不同的。这种共同的-特殊的分解提供了一种将大量数据压缩到可管理的因素数量的有效方法。目前可用于因子分析的统计结果假定面板的时间或横截面尺寸较小。这项研究开发了当数据面板的两个维度都很大时进行因子分析的工具。我们展示了如何通过主成分方法从数据中一致地估计公共和特殊成分，尽管没有观察到，无论数据是否是平稳的。我们将制定统计标准，从数据中确定未知因素的数量。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。许多宏观和金融经济学的问题都可以在一个因素框架内进行研究。例如，经济周期的特点是大量经济时间序列的协动。资产回报已被证明具有一种因素结构，特殊变量是可以多样化的，而系统性变量则不是。全球趋势和全球经济衰退等概念经常被使用。要素框架提供了对这些概念的正式处理。通过为大维度的因素分析提供统计基础，我们的结果使研究人员能够使用数十年的数百个序列、几年的数千个资产收益序列和数百个国家水平的序列来估计因素并进行推断。这项研究的结果将使最大限度地利用现有信息成为可能，而不必主观地选择要分析的序列。

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.