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Recovering cointegration via wavelets in the presence of non-linear patterns

Jorge Martínez Compains EMAIL logo , Ignacio Rodríguez Carreño ORCID logo , Ramazan Gençay , Tommaso Trani ORCID logo and Daniel Ramos Vilardell


Johansen’s Cointegration Test (JCT) performs remarkably well in finding stable bivariate cointegration relationships. Nonetheless, the JCT is not necessarily designed to detect such relationships in presence of non-linear patterns such as structural breaks or cycles that fall in the low frequency portion of the spectrum. Seasonal adjustment procedures might not detect such non-linear patterns, and thus, we expose the difficulty in identifying cointegrating relations under the traditional use of JCT. Within several Monte Carlo experiments, we show that wavelets can empower more the JCT framework than the traditional seasonal adjustment methodologies, allowing for identification of hidden cointegrating relationships. Moreover, we confirm these results using seasonally adjusted time series as US consumption and income, gross national product (GNP) and money supply M1 and GNP and M2.

JEL Classification: C01; C12; C22

Corresponding author: Jorge Martínez Compains, Department of Economics, Simon Fraser University, Vancouver, Canada, E-mail:

Ramazan Gençay: Deceased.

Funding source: Ministerio de Economía, Industria y Competitividad

Award Identifier / Grant number: ECO 2015-68815-P

Award Identifier / Grant number: ECO 2017-83183-R


The authors are grateful to the Editor and an anonymous referee for his comments. They thank seminar and conference participants at the Simon Fraser University and İstanbul Bilgi University. Ignacio Rodríguez Carreno thanks the Department of Economics of Simon Fraser University, where part of this research was conducted, for their hospitality. Finally, special thanks to our friend Ramo, in memoriam.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: Ignacio Rodriguez Carreño also gratefully acknowledges the financial support received from the Ministerio de Economía, Industria y Competitividad (ECO 2017-83183-R). Tommaso Trani gratefully acknowledges the financial support received from the Ministerio de Economía, Industria y Competitividad (ECO 2015-68815-P).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


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Supplementary Material

The online version of this article offers supplementary material (

Received: 2018-12-12
Accepted: 2021-09-21
Published Online: 2021-10-15

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