Collaborative Research: Topics in Factor Analysis of Large Dimensions

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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.