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现有数据量的增加。以前开发的用于处理少数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实证工具，可以综合数据简洁，方便经济分析的方式。 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。这种共同的特质分解提供了一种有效的方法，将大量的数据压缩到一个可管理的因素数量。 目前可用于因子分析的统计结果假设面板的时间或横截面尺寸很小。本研究开发了当数据面板的两个维度都很大时进行因素分析的工具。我们展示了如何共同的和特质的组成部分，虽然未观察到的，可以一致地估计从数据的主成分的方法是否数据是平稳的。我们将开发统计标准，用于从数据中确定未知数量的因素。我们还将开发测试，以确定在观察到的数据的非平稳性是常见的或特殊的类型。我们将建立主成分估计量的统计性质。我们亦会考虑不同的公共因素估计方法，在一个因素架构内，可以研究宏观经济及金融经济的许多问题。例如，商业周期的特点是大量经济时间序列的共同运动。资产收益已被证明有一个因素结构，与特质的变化是多样化的，而系统的不是。全球趋势和全球经济衰退等概念经常被使用。因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来的数百个系列，多年来的数千个资产回报率以及数百个国家级系列来估计因素并进行推断。这项研究的结果将使人们能够最大限度地利用可用信息，而不必主观选择要分析的系列。

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.