Statistical Learning for Big Dependent Data

CHAPTER 6DYNAMIC FACTOR MODELS

Factor models (FM) were introduced by Charles Spearman, a British psychologist, in the first quarter of the twentieth century to explain the concept of intelligence. He found that the results of different people in a set of tests of mental capacity could be explained by a general factor, which he called factor for intelligence, and a specific component, that depends on the class of test. FMs were mainly studied first in psychology, then in economics for studying the dimension of economic development, and in sociology for understanding social and economic concepts. See, Harman (1976) for further information.

Early factor analysis for time series includes Anderson (1963), that recognized the need of developing specific results for time series data such as lag factor effects, and Brillinger (1964), who introduced dynamic principal components (DPCs) for time series. Geweke (1977) proposed a dynamic factor model (DFM) for stationary time series assuming that each variable is the sum of two independent components: a common component, generated by factors, plus a specific component, or noise. The factors are assumed to follow independent linear processes ...