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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

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Volume 19, Issue 5


Amplitude and phase synchronization of European business cycles: a wavelet approach

Joanna Bruzda
Published Online: 2015-05-21 | DOI: https://doi.org/10.1515/snde-2014-0081


In the paper we suggest the use of amplitude correlation coefficients (ACCs) and phase-locking values (PLVs) in examining business cycle synchronization. The quantities are calculated on the basis of instantaneous amplitudes and phase differences, which are computed here with the help of the non-decimated discrete analytic wavelet transform. We show that the coefficients constitute an interesting add-in to the statistical apparatus of examining business cycle synchronization. The PLVs correct the information provided by the coherency and correlation coefficients for the influence of amplitude changes and are of use in examining phase synchronization of business cycles, which is important in forecasting the effectiveness of a common monetary policy. By contrast, the ACCs are based solely on amplitude information and have the interpretation of phase-adjusted correlation coefficients, which can be used to evaluate stabilization policies or to forecast these policies’ effectiveness. The methodology is applied to examine cyclical synchronization of 20 European Union (EU) countries. We show, among other things, that during the run-up to the euro both amplitude and phase synchronization increased, with the former tending to change more rapidly. Furthermore, for the new EU members an EU effect is identified in both types of cyclical synchronization with the euro area.

This article offers supplementary material which is provided at the end of the article.

Keywords: amplitude synchronization; business cycle; phase synchronization; wavelets

JEL codes: C14; C38; E32; O52


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About the article

Corresponding author: Joanna Bruzda, Nicolaus Copernicus University, Gagarina 11, 87-100 Torun, Poland, e-mail:

Published Online: 2015-05-21

Published in Print: 2015-12-01

Citation Information: Studies in Nonlinear Dynamics & Econometrics, Volume 19, Issue 5, Pages 625–655, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2014-0081.

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