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The Generalized Dynamic Factor Model: Representation Theory

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  • Lippi, Marco
  • Forni, Mario

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.

Suggested Citation

  • Lippi, Marco & Forni, Mario, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:2509
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    Keywords

    Dynamic factor structure; Dynamic principal components; Idiosyncratic components; Large cross-sections;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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