Dynamic Factor Models with Infinite-Dimensional Factor Space: Asymptotic Analysis

Marco Lippi, Marc Hallin, Mario Forni and Paolo Zaffaroni

No 10618, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni, Hallin, Lippi and Reichlin (2004). Those estimators, however, rely on Brillinger's dynamic principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard (static) principal components, which have been dominant in this literature. On the other hand, the consistency of those static estimators requires the assumption that the space spanned by the factors has finite dimension, which severely restricts the generality afforded by the GDFM. This paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one-sided filters recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015). Consistency and exact rates of convergence are obtained for this estimator, under a general class of GDFMs that does not require a finite-dimensional factor space. A Monte Carlo experiment corroborates those theoretical results and demonstrates the excellent performance of those estimators in out-of-sample forecasting.

Keywords: Consistency and rates.; Generalized dynamic factor models.; High -dimensional time series.; One-sided representations of dynamic factor models.; Vector processes with singular spectral density (search for similar items in EconPapers)
JEL-codes: C0 C01 E0 (search for similar items in EconPapers)
Date: 2015-05
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for and nep-mac
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Citations: View citations in EconPapers (61)

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Related works:
Journal Article: Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis (2017)
Working Paper: Dynamic Factor Models with Infinite-Dimensional Factor Space. Asymptotic Analysis (2016)
Working Paper: Dynamic Factor Models with Infinite-Dimensional Factor Space: Asymptotic Analysis (2015)
Working Paper: Dynamic Factor Models with In nite-Dimensional Factor Space: Asymptotic Analysis (2015)
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