A Measure of Comovement for Economic Variables: Theory and Empirics

28 Pages Posted: 20 Dec 2001

See all articles by Christophe Croux

Christophe Croux

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES); Catholic University of Leuven (KUL) - Department of Applied Economics

Mario Forni

Università degli studi di Modena e Reggio Emilia (UNIMORE) - Faculty of Business and Economics; Centre for Economic Policy Research (CEPR)

Lucrezia Reichlin

London Business School; Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES); Centre for Economic Policy Research (CEPR); European Central Bank (ECB)

Date Written: December 1999

Abstract

This paper proposes a measure of dynamic comovement between (possibly many) time series and names it cohesion. The measure is defined in the frequency domain and is appropriate for processes that are costationary, possibly after suitable transformations. In the bivariate case, the measure reduces to dynamic correlation and is related, but not equal, to the well known quantities coherence and coherency. Dynamic correlation on a frequency band equals (static) correlation of band-pass filtered series. Moreover, long run correlation and cohesion relate in a simple way to cointegration. Cohesion is useful to study problems of business cycle synchronization, to investigate short-run and long-run dynamic properties of multiple time series, to identify dynamic clusters. We use state income data for the US and GDP data for European nations to provide an empirical illustration focused on the geographical aspects of business cycle fluctuations.

Keywords: Business cycle, coherence, comovements, geography

JEL Classification: C10, E32

Suggested Citation

Croux, Christophe and Forni, Mario and Reichlin, Lucrezia, A Measure of Comovement for Economic Variables: Theory and Empirics (December 1999). Available at SSRN: https://ssrn.com/abstract=223578

Christophe Croux

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

Catholic University of Leuven (KUL) - Department of Applied Economics ( email )

Leuven, B-3000
Belgium

Mario Forni (Contact Author)

Università degli studi di Modena e Reggio Emilia (UNIMORE) - Faculty of Business and Economics ( email )

Viale Berengario 51
41100 Modena, Modena 41100
Italy
+39 059 205 6852 (Phone)
+39 059 205 6947 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Lucrezia Reichlin

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

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
+32 2 650 4221 (Phone)
+32 2 650 4475 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany

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