THE GENERALIZED DYNAMIC FACTOR MODEL: REPRESENTATION THEORY
By M. Forni, Marco Lippi. Econometric Theory, 2001
428 citations recorded by the source corpus.
This paper, along with the companion paper Forni, Hallin, Lippi, and Reichlin (2000, Review of Economics and Statistics 82, 540–554), 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, Econometrica 51, 1181–1304) and Chamberlain and Rothschild (1983, Econometrica 51, 1305–1324) by allowing serial correlation within and across individual processes and of the dynamic factor model of Sargent and Sims (1977, in C.A. Sims (ed.), New Methods in Business Cycle Research, pp. 45–109) and Geweke (1977, in D.J. Aigner & A.S. Goldberger (eds.), Latent Variables in Socio-Economic Models, pp. 365–383) by allowing for nonorthogonal idiosyncratic terms. Whereas 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.
Subfields: Economics and Econometrics
View Paper: https://www.semanticscholar.org/paper/d1e7df46abc62130b8fc12d8edc7e9bd26fac09f
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Citations in the corpus
- Asymptotics of the principal components estimator of large factor models with weakly influential factors (2012, background): “For example, in the spirit of Forni and Lippi (1999, 2001), consider an nindustry constant-returns economy, where the productionsXit in industries i = 1; :::; n at time t are given by the equations:0BBBB@ 1 w12 : : : w1n w21 1 : : : w2n ... ... . . . ... wn1 wn2 : : : 1 1CCCCA 0BBBB@ X1t X2t…”
- Weak and Strong Cross Section Dependence and Estimation of Large Panels (2011, background): “The idiosyncratic (or weak dependence) property, advanced by Forni and Lippi (2001), applies to both dimensions and requires that the weighted average of a stationary process, computed both over time and across sections, converges to zero in quadratic mean for all sets of weights satisfying a…”
- The Dynamic Effects of Monetary Policy: A Structural Factor Model Approach (2010, background): “FGLR is a special case of the generalized dynamic factor model proposed by Forni et al. (2000) and Forni and Lippi (2001).”
- Change-point detection in panel data via double CUSUM statistic (2016, background): “(2000) steps further and admits the following representation theorem (Forni and Lippi 2001): any εt with a finite number (q <∞) of diverging dynamic eigenvalues is decomposed into χt driven by a q-tuple of white noises ut (common shocks) as χt = b(L)ut (L denotes the lag operator and b(L) is an n× q”
- PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS (2014, methodology): “atson (2002), Bai (2003), Bai and Ng (2002), Breitung and Tenhofen (2011), Lam and Yao (2012) among others. In this paper, we consider static factor model, which differs from the dynamic factor model [Forni and Lippi (2001), Forni et al. (2000, 2015)]. The dynamic model allows more general infinite di”
- A network analysis of the volatility of high dimensional financial series (2017, methodology): “…versions of those methods have become daily practice in many areas of econometrics and finance; among these the GDFM by Forni et al. (2000) and Forni and Lippi (2001) is the most general, whereas most other factor models that have been considered in the time series literature (Stock and…”
- Theory and Practice of GVAR Modeling (2016, neutral): “…in the vector xt′ belong to Ωt0 and the last kb = k − ka variables do not, and let us partition εt as εt = (ε′at, ε′bt) ′ and the covariance matrix 14See also Forni and Lippi (2001), Forni et al. (2000), Forni et al. (2004), Stock and Watson (1999), Stock and Watson (2002), Giannone, Reichlin,…”
- Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit (2013, methodology): “Factor models are examples of the former (see Forni and Lippi, 2001; Forni et al., 2000, 2004; Geweke, 1977; Sargent and Sims, 1977).”
- No News in Business Cycles (2014, neutral): “Early references are Forni and Reichlin (1998), Forni, Hallin, Lippi and Reichlin (2000), Forni and Lippi (2001), Stock and Watson (2002a, 2002b), Bai and Ng (2002).”
- A generalised dynamic factor model for the Belgian economy - Useful business cycle indicators and GDP growth forecasts (2006, methodology): “The representation theory can be found in Forni and Lippi (2001).”
- Principal Component Analysis of High-Frequency Data (2016, background): “A real-valued function F defined on a subset of M+d is called a spectral function (see, e.g., Friedland 1981) if for any orthogonal matrixO inMd andX inM+d , F(X ) = F(OᵀXO).”
- Comparing Alternative Predictors Based on Large-Panel Factor Models (2012, positive): “However, if data follow an approximate dynamic factor model, the set of common factors Ft can be consistently estimated by appropriate crosssectional averages, or aggregators in the terminology of Forni and Reichlin (1998) and Forni and Lippi (2001).”
- A Core Inflation Indicator for the Euro Area (2005, neutral): “Forni et al., 2000, 2002, and Forni and Lippi, 2001).”
- Exponent of Cross-Sectional Dependence: Estimation and Inference (2016, positive): “An important strand in the empirical factor literature, promoted through the work of Forni, Hallin, Lippi, and Reichlin (2000), Forni and Lippi (2001) and Stock and Watson (2002), uses factor models to forecast a few key macro variables such as output growth, inflation or unemployment rate with a…”