Dynamic Factor Models, Cointegration, and Error Correction Mechanisms

29 Pages Posted: 22 Mar 2016

See all articles by Matteo Barigozzi

Matteo Barigozzi

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES); London School of Economics and Political Science; University of Bologna

Marco Lippi

Dipartimento di Scienze Economiche (DiSSE); Einaudi Institute for Economics and Finance (EIEF)

Matteo Luciani

Board of Governors of the Federal Reserve System

Multiple version iconThere are 2 versions of this paper

Date Written: 2016-02-16

Abstract

The paper studies Non-Stationary Dynamic Factor Models such that: (1) the factors Ft are I(1) and singular, i.e. Ft has dimension r and is driven by a q-dimensional white noise, the common shocks, with q < r, and (2) the idiosyncratic components are I(1). We show that Ft is driven by r-c permanent shocks, where c is the cointegration rank of Ft, and q - (r - c) < c transitory shocks, thus the same result as in the non-singular case for the permanent shocks but not for the transitory shocks. Our main result is obtained by combining the classic Granger Representation Theorem with recent results by Anderson and Deistler on singular stochastic vectors: if (1 - L)Ft is singular and has rational spectral density then, for generic values of the parameters, Ft has an autoregressive representation with a finite-degree matrix polynomial fulfilling the restrictions of a Vector Error Correction Mechanism with c error terms. This result is the basis for consistent estimation of Non-Stationary Dynamic Factor Models. The relationship between cointegration of the factors and cointegration of the observable variables is also discussed.

Keywords: Cointegration for singular vectors, Dynamic Factor Models for I(1) variables, Granger Representation Theorem for singular vectors

JEL Classification: C01, E00

Suggested Citation

Barigozzi, Matteo and Barigozzi, Matteo and Barigozzi, Matteo and Lippi, Marco and Luciani, Matteo, Dynamic Factor Models, Cointegration, and Error Correction Mechanisms (2016-02-16). FEDS Working Paper No. 2016-018, Available at SSRN: https://ssrn.com/abstract=2752861 or http://dx.doi.org/10.17016/FEDS.2016.018

Matteo Barigozzi (Contact Author)

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Marco Lippi

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Einaudi Institute for Economics and Finance (EIEF) ( email )

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Matteo Luciani

Board of Governors of the Federal Reserve System ( email )

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