Inferential theory for generalized dynamic factor models

Manfred Deistler and the General-Dynamic-Factor-Model Approach to the Statistical Analysis of High-Dimensional Time Series

“…Surprisingly, the consistency rates are comparable to those obtained by Bai (2003) for the static method (without the preliminary filtering (11))the validity of which, however, requires the much more stringent assumptions of the static model ( 8). The same results also apply in the identification and estimation of volatilities Barigozzi and Hallin (2016, of time-varying GDFMs Barigozzi et al (2021a), and in the prediction of conditional variances, values at risk, and expected shortfalls Hallin and Trucíos (2022); Trucíos et al (2022).…”

“…Anderson and Deistler (2008a) only briefly mention, without entering into details, the relevance of their result for the general dynamic factor model (with dynamic loadings as in ( 7)). That relevance is further discussed in Deistler (2008b, 2009), Deistler et al (2010), and Forni and Lippi (2011; it is fully exploited in Forni et al (2015Forni et al ( , 2017Forni et al ( , 2018, Barigozzi et al (2021aBarigozzi et al ( , 2021b, and several subsequent papers. The same result also has important consequences in the macroeconomic applications of factor models and the estimation and identification of structural VARs: see Forni et al (2020).…”

A Conversation With Marc Hallin

“…I also should mention several papers with Matteo Barigozzi, a student of Marco's, where factor model techniques are applied to the analysis of volatility in high-dimensional time series, for example, Barigozzi & Hallin (2016,2019,2021, as well as a few others with Carlos Trucíos on the prediction of large covariance matrices and value-atrisk in large portfolios; see, for example, Hallin & Trucios (2023) Sargent & Sims (1977), Chamberlain (1983), and Chamberlain & Rothschild (1983). Their modern versions are mainly due to Forni et al (2000), Stock & Watson (2002a, 2002b, and Bai (2003); see Barigozzi & Hallin (2023) for details.…”

“…Marc : Dynamic factor models originated in four pathbreaking papers, namely, Geweke (1977), Sargent & Sims (1977), Chamberlain (1983), and Chamberlain & Rothschild (1983). Their modern versions are mainly due to Forni et al (2000), Stock & Watson (2002a, 2002b), and Bai (2003); see Barigozzi & Hallin (2023) for details.…”

“…In contrast to traditional covariance‐based principal components, it is related to Brillinger's frequency domain concept of dynamic principal components (Brillinger, 1964; 1981). For a complete inferential theory, see Barigozzi et al (2024a).…”