The Generalized Dynamic Factor Model: Representation Theory

Marco Lippi and Mario Forni

No 2509, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: This paper, along with the companion paper Forni, Hallin, Lippi and Reichlin (1999), introduces a new model-the generalized dynamic factor model-for the empirical analysis of financial and macroeconomic data sets characterized by a large number of observations both cross-section and over time. This model provides a generalization of the static approximate factor model of Chamberlain (1983) and Chamberlain and Rothschild (1983) by allowing serial correlation within and across individual processes, and of the dynamic factor model of Sargent and Sims (1977) and Geweke (1977) by allowing for non-orthogonal idiosyncratic terms. While the companion paper concentrates on identification and estimation, here we give a full characterization of the generalized dynamic factor model in terms of observable spectral density matrices, thus laying a firm basis for empirical implementation of the model. Moreover, the common factors are obtained as limits of linear combinations of dynamic principal components. Thus the paper reconciles two seemingly unrelated statistical constructions.

Keywords: Dynamic factor structure; Dynamic principal components; Idiosyncratic components; Large cross-sections (search for similar items in EconPapers)
JEL-codes: C13 C33 C43 (search for similar items in EconPapers)
Date: 2000-07
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Citations: View citations in EconPapers (255)

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Journal Article: THE GENERALIZED DYNAMIC FACTOR MODEL: REPRESENTATION THEORY (2001)
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