Testing for Common Cyclical Features in VAR Models with Cointegration

31 Pages Posted: 23 May 2001

See all articles by Alain Hecq

Alain Hecq

Maastricht University - Department of Economics

Franz C. Palm

University of Maastricht - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Jean-Pierre Urbain

Maastricht University - Department of Economics

Date Written: April 2001

Abstract

We consider VAR models for variables exhibiting cointegration and common cyclical features. While the presence of cointegration reduces the rank of the long-run multiplier matrix, other types of common features lead to rank reduction of the short-run dynamics. We distinguish between strong and weak form reduced rank structures. Strong form reduced rank structures analyzed by Engle and Kozicki (1993) arise when a linear combination of the first differenced variables in a cointegrated VAR is white noise whereas in the presence of a weak form reduced rank structure, linear combinations of the first differenced variables corrected for the long-run effects are white noise. The weak form has an interest in its own. For instance, it is a necessary condition for the existence of first order codependent cycles in a VAR(2). Also, it is a necessary condition for the strong form. We also consider the mixed form which combines strong and weak forms. We discuss the model selection issues which arise from this distinction and propose a simple approach to testing for these structures using a sequence of likelihood ratio test statistics. The finite sample behavior of the sequential approach is analyzed in a Monte Carlo experiment. Finally, we illustrate the relevance of the different forms of reduced ranks with an empirical analysis of US business uctuations over the period 1954-1996.

Keywords: Serial Correlation Common Features, Reduced Rank Structure, Cointegration

JEL Classification: C32

Suggested Citation

Hecq, Alain and Palm, Franz C. and Urbain, Jean-Pierre, Testing for Common Cyclical Features in VAR Models with Cointegration (April 2001). Available at SSRN: https://ssrn.com/abstract=270177

Alain Hecq

Maastricht University - Department of Economics

P.O. Box 616
Maastricht, 6200 MD
Netherlands

Franz C. Palm (Contact Author)

University of Maastricht - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands
+31-(0)43-3883833 (Phone)
+31-(0)43-3258535 (Fax)

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.cesifo.de

Jean-Pierre Urbain

Maastricht University - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

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