The generalized dynamic factor model: consistency and rates

By M. Forni, Marc Hallin, Marco Lippi, L. Reichlin. 2004

327 citations recorded by the source corpus.

Abstract A factor model generalizing those proposed by Geweke (in: D.J. Aigner and A.S. Goldberger, Latent Variables in Socio-Economic Models, North-Holland, Amsterdam, 1977), Sargent and Sims (New Methods in Business Research, Federal Reserve Bank of Minneapolis, Minneapolis, 1977), Engle and Watson (J. Amer. Statist. Assoc. 76 (1981) 774) and Stock and Watson (J. Business. Econom. Statist. 20 (2002) 147) has been introduced in Forni et al. (Rev. Econ. Statist. 80 (2000) 540), where consistent (as the number n of series and the number T of observations both tend to infinity along appropriate paths (n,T(n))) estimation methods for the common component are proposed. Rates of convergence associated with these methods are obtained here as functions of the paths (n,T(n)) along which n and T go to infinity. These results show that, under suitable assumptions, consistency requires T(n) to be at least of the same order as n, whereas an optimal rate of n is reached for T(n) of the order of n2. If convergence to the space of common components is considered, consistency holds irrespective of the path (T(n) thus can be arbitrarily slow); the optimal rate is still n , but only requires T(n) to be of the order of n.

Subfields: Economics and Econometrics, Marketing

View Paper: https://www.semanticscholar.org/paper/77f941ca77436f1b2c09c392a86546d69c1b202e

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Citations in the corpus

Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit (2013, unknown): “Factor models are examples of the former (see Forni and Lippi, 2001; Forni et al., 2000, 2004; Geweke, 1977; Sargent and Sims, 1977).”
Factor modeling for high-dimensional time series: inference for the number of factors (2012, background): “Hallin and Liska (2007) proposed an information criterion to determine r.”
Opening the Black Box: Structural Factor Models Versus Structural Vars (2003, methodology): “Assumptions PA2 and FM4 are technical and do not entail a severe loss of generality (see Forni et al., 2002b for additional details).”
Forecasting with Many Predictors (2006, background): “Forni et al. (2000, 2004) study the properties of this algorithm and the estimator of the common component of Xit in a DFM, λi(L)′ft , when n is large.”
On the Marčenko-Pastur law for linear time series (2013, background): “[13, 14, 15], and Stock and Watson [33], to name a few.”
A parametric estimation method for dynamic factor models of large dimensions (2009, methodology): “We refer to Forni and Lippi (2001) and Forni et al. (1999, 2000, 2004) for a treatment of the more general dynamic case.”
Random matrix theory in statistics: A review (2014, methodology): “A more enhanced version of the factor analysis model, the so-called dynamic factor model, is used extensively in econometrics, where the factors f are taken to be time-dependent (Forni et al., 2000, 2004, 2005).”
Forecasting Inflation in a Data-Rich Environment: The Benefits of Machine Learning Methods (2019, methodology): “…power, theoretical developments in ML, and availability of large datasets, researchers have started to consider the usage of high-dimensional models on top of the well-established (dynamic) factor models of Stock & Watson (2002), Bai & Ng (2003, 2006), and Reichlin et al. (2000, 2004).”
Are Disaggregate Data Useful for Factor Analysis in Forecasting French GDP (2010, methodology): “Forni et al. (2004, 2005) To estimate the dynamic factors and their covariances, FHLR(2000, 2001, 2004, 2005) propose dynamic principal analysis in the frequency domain.”
A two-step estimator for large approximate dynamic factor models based on Kalman filtering (2011, unknown): “We suppose that the common component is pervasive, in the following sense: (CR1) lim infn→∞ 1nλmin(Λ ∗ ′ 0 Λ ∗ 0) > 0 We also suppose, as in Forni et al. (2004), that all the eigenvalues of Λ∗ ′0 Λ ∗ 0 diverge at the same rate, which is equivalent to the following further assumption: (CR2) lim…”