Dynamic Factor Models, Cointegration, and Error Correction Mechanisms

28 Pages Posted: 1 Mar 2014 Last revised: 29 Feb 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: February 16, 2016

Abstract

The paper studies Non-Stationary Dynamic Factor Models such that: (1) the factors F_t are I(1) and singular, i.e. F_t 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 F_t is driven by r − c permanent shocks, where c is the cointegration rank of F_t, 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)F_t is singular and has rational spectral density then, for generic values of the parameters, F_t 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: Dynamic Factor Models for I(1) variables, Cointegration, Granger Representation Theorem

JEL Classification: C0, C01, E0

Suggested Citation

Barigozzi, Matteo and Barigozzi, Matteo and Barigozzi, Matteo and Lippi, Marco and Luciani, Matteo, Dynamic Factor Models, Cointegration, and Error Correction Mechanisms (February 16, 2016). Available at SSRN: https://ssrn.com/abstract=2402185 or http://dx.doi.org/10.2139/ssrn.2402185

Matteo Barigozzi (Contact Author)

University of Bologna ( email )

Piazza Scaravilli 2
Bologna, 40100
Italy

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES) ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium

HOME PAGE: http://www.barigozzi.eu/research.html

London School of Economics and Political Science ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

Marco Lippi

Dipartimento di Scienze Economiche (DiSSE) ( email )

14 Via Cesalpino
Rome, 00161
Italy
+39 06 4428 4202 (Phone)
+39 06 4404 572 (Fax)

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

Via Due Macelli, 73
Rome, 00187
Italy

Matteo Luciani

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
140
Abstract Views
838
rank
189,820
PlumX Metrics