Skip to main content
Article
Licensed
Unlicensed Requires Authentication

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

  • EMAIL logo
Published/Copyright: May 21, 2015
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Studies in Nonlinear Dynamics & Econometrics
From the journal Studies in Nonlinear Dynamics & Econometrics Volume 19 Issue 5

Abstract

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.

Keywords: amplitude synchronization; business cycle; phase synchronization; wavelets
JEL codes: C14; C38; E32; O52
Corresponding author: Joanna Bruzda, Nicolaus Copernicus University, Gagarina 11, 87-100 Torun, Poland, e-mail:

Acknowledgments

The author acknowledges the financial support from the Polish National Science Center obtained under decision no. DEC-2013/09/B/HS4/02716. The paper has benefited from discussions with Maciej Ryczkowski from the Nicolaus Copernicus University in Toruń as well as helpful, encouraging, and constructive suggestions of the Referees.

Funding: Polish National Science Center, (Grant/Award Number: DEC-2013/09/B/HS4/02716).

Annex

This annex provides a detailed description of the three datasets used in the study.

The first set comprises the GDP estimates from the Quarterly National Accounts database available at the OECD statistical portal. The series used are “Historical GDP – expenditure approach” (B1_GE) in millions of national currency, volume estimates, seasonally adjusted (denoted in the database as VOBARSA). This set of quarterly data covers time series for the 15 old member states of the EU (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden, and the UK), for which the data span the period 1960.I–2014.III (219 observations), except for Luxembourg, where the data end in 2014.II, as well as five new UE member states: the Czech Republic (1994.I–2014.III; 83 observations), Hungary (1995.I–2014.III; 79 observations), Poland (1995.I–2014.III; 79 observations), Slovakia (1993.I–2014.III; 87 observations), Slovenia (1995.I–2014.III; 79 observations), and the euro area (18 countries; 1995.I–2014.III; 79 observations).

The second dataset covers IP indexes for the 20 countries under study and the euro area (18 countries) from the Main Economic Indicators database of the OECD. The variable used is the seasonally adjusted “Production of Total Industry.” Taking into consideration the availability of the data, the maximum possible time period of analysis for all the 15 old EU member states is July 1975 through September 2014, and this is the data span used here (471 monthly observations). The euro area aggregate is also available in this time period. The time series for the remaining five countries are much shorter and cover the following periods: the Czech Republic – 1990.01–2014.09 (297 observations), Hungary – 1985.01–2014.09 (357 observations), Poland – 1985.01–2014.09 (357 observations), Slovakia – 1989.01–2014.09 (309 observations), and Slovenia – 1992.01–2014.09 (273 observations).

The last set of data comprises the monthly ESI series available at the European Commission portal. The ESI is a composite indicator computed as a weighted average of five seasonally adjusted survey-based confidence indicators: Industrial Confidence Indicator (40%), Services Confidence Indicator (30%), Consumer Confidence Indicator (20%), Construction Confidence Indicator (5%), and Retail Trade Confidence Indicator (5%). The time period covered by this dataset changes from country to country and also extends slightly further in time as compared to the previous sets. The longest time series, available for Austria, Belgium, Denmark, Finland, Germany, Greece, Italy, Luxembourg, the Netherlands, the UK, and the euro area, contain data from the period 1985.01 to 2014.11 (359 observations), whereas, for the other countries under study, the time periods covered are the following: France – 1985.02–2014.11 (358 observations), Portugal – 1987.01–2014.11 (335 observations), Spain – 1987.04–2014.11 (332 observations), Sweden – 1990.01–2014.11 (299 observations), the Czech Republic – 1995.01–2014.11 (239 observations), Hungary – 1996.01–2014.11 (227 observations), Poland – 1993.10–2014.11 (254 observations), Slovakia – 1993.08–2014.11 (256 observations), and Slovenia – 1995.04–2014.11 (236 observations). This set does not contain data for Ireland.

References

Adhikari, A., T. Sigurdsson, M. A. Topiwala, and J. A. Gordon. 2010. “Cross-Correlation of Instantaneous Amplitudes of Field Potential Oscillations: A Straightforward Method to Estimate the Directionality and Lag Between Brain Areas.” Journal of Neuroscience Methods 191: 191–200. doi:10.1016/j.jneumeth.2010.06.019.10.1016/j.jneumeth.2010.06.019Search in Google Scholar PubMed PubMed Central

Afonso, A., and D. Furceri 2009. “Sectoral Business Cycle Synchronization in the European Union.” Economics Bulletin 29 (4): 2996–3014.Search in Google Scholar

Aguiar-Conraria, L., and M. J. Soares. 2011. “Business Cycle Synchronisation and the Euro: A Wavelet Analysis.” Journal of Macroeconomics 33: 477–489. doi:10.1016/j.jmacro.2011.02.005.10.1016/j.jmacro.2011.02.005Search in Google Scholar

Aguiar-Conraria, L., M. M. F. Martins, and M. J. Soares. 2013. “Convergence of Economic Sentiment Cycles in the Eurozone: A Time-Frequency Analysis.” Journal of Common Market Studies 51: 377–398. doi:10.1111/j.1468-5965.2012.02315.x.10.1111/j.1468-5965.2012.02315.xSearch in Google Scholar

Aslanidis, N. 2010. “Business Cycle Synchronization Between the CEEC and the Euro-Area: Evidence from Threshold Seemingly Unrelated Regressions.” The Manchester School 78: 538–555. doi:10.1111/j.1467-9957.2009.02149.x.10.1111/j.1467-9957.2009.02149.xSearch in Google Scholar

Bekiros, S., D. K. Nguyen, G. S. Uddin, and B. Sjö. 2015. “Business Cycle (De)Synchronization in the Aftermath of the Global Financial Crisis: Implications for the Euro Area.” Studies in Nonlinear Dynamics and Econometrics 19 (5): 609–624. doi:10.1515/snde-2014-0055.10.1515/snde-2014-0055Search in Google Scholar

Bruns, A. 2004. “Fourier-, Hilbert- and Wavelet-Based Signal Analysis: Are They Really Different Approaches?” Journal of Neuroscience Methods 137: 321–332. doi:10.1016/j.jneumeth.2004.03.002.10.1016/j.jneumeth.2004.03.002Search in Google Scholar PubMed

Bruzda, J. 2011a. “Some Aspects of the Discrete Wavelet Analysis of Bivariate Spectra for Business Cycle Synchronisation.” Economics – The Open-Access, Open-Assessment E-Journal 5: 1–46. doi:10.5018/economics-ejournal.ja.2011-16.10.5018/economics-ejournal.ja.2011-16Search in Google Scholar

Bruzda, J. 2011b. “Business Cycle Synchronization According to Wavelets – The Case of Poland and the Euro Zone Member Countries.” Bank & Credit 42: 5–32. http://www.bankikredyt.nbp.pl/content/2011/03/bik_03_2011_01_art.pdf.Search in Google Scholar

Bruzda, J. 2013. Wavelet Analysis in Economic Applications. Toruń: Toruń University Press.Search in Google Scholar

Bruzda, J. 2014a. “On Simple Wavelet Estimators of Random Signals and Their Small-Sample Properties.” Journal of Statistical Computation and Simulation, in press, doi:10.1080/00949655.2014.941843.10.1080/00949655.2014.941843Search in Google Scholar

Bruzda, J. 2014b. “Real- and Complex-Valued Discrete Wavelets in Asset Classification. Some Methodological Remarks with Example.” Working Paper, Nicolaus Copernicus University in Toruń. http://ssrn.com/abstract=2571575.10.2139/ssrn.2571575Search in Google Scholar

Croux, C., M. Forni, and L. Reichlin. 2001. “A Measure of Comovement for Economic Variables: Theory and Empirics.” Review of Economics and Statistics 83: 232–241. doi:10.1162/00346530151143770.10.1162/00346530151143770Search in Google Scholar

Crowley, P. M., and D. G. Mayes. 2008. “How Fused Is the Euro Area Core? An Evaluation of Growth Cycle Co-Movement and Synchronization Using Wavelet Analysis.” Journal of Business Cycle Measurement and Analysis 4: 63–95. doi:10.1787/jbcma-v2008-art4-en.10.1787/jbcma-v2008-art4-enSearch in Google Scholar

de Haan, J., R. Inklaar, and R. Jong-A-Pin. 2008. “Will Business Cycles in the Euro Area Converge? A Critical Survey of Empirical Research.” Journal of Economic Surveys 22: 234–273. doi: 10.1111/j.1467-6419.2007.00529.x.10.1111/j.1467-6419.2007.00529.xSearch in Google Scholar

Fidrmuc, J., and I. Korhonen I. 2006. “Meta-Analysis of the Business Cycle Correlation Between the Euro Area and the CEECs.” Journal of Comparative Economics 34: 518–537. doi:10.1016/j.jce.2006.06.007.10.1016/j.jce.2006.06.007Search in Google Scholar

Gächter, M., A. Riedl, and D. Ritzberger-Grünwald. 2013. “Business Cycle Convergence or Decoupling? Economic Adjustment in CESEE During the Crisis.” BOFIT Discussion Papers 3, Bank of Finland. www.suomenpankki.fi/bofit_en/tutkimus/tutkimusjulkaisut/dp/pages/dp0313.aspx.10.2139/ssrn.2235041Search in Google Scholar

Gallegati, M. 2008. “Wavelet Analysis of Stock Returns and Aggregate Economic Activity.” Computational Statistics & Data Analysis 52: 3061–3074. doi:10.1016/j.csda.2007.07.019.10.1016/j.csda.2007.07.019Search in Google Scholar

Gallegati, M., and M. Gallegati. 2007. “Wavelet Variance Analysis of Output in G-7 Countries.” Studies in Nonlinear Dynamics and Econometrics 11 (3): article 6. doi:10.2202/1558-3708.1435.10.2202/1558-3708.1435Search in Google Scholar

Gayer, C. 2007. “A Fresh Look at Business Cycle Synchronization in the Euro Area.” European Economy – Economic Paper 287, European Commission. http://ec.europa.eu/economy_finance/publications/publication_summary9501_en.htm.Search in Google Scholar

Gençay, R., and N. Gradojevic. 2011. “Errors-in-Variables Estimation with Wavelets.” Journal of Statistical Computation and Simulation 81: 1545–1564. doi:10.1080/00949655.2010.495073.10.1080/00949655.2010.495073Search in Google Scholar

Gençay R., and D. Signori. 2015. “Multi-Scale Tests for Serial Correlation.” Journal of Econometrics 184(1): 62–80. doi:10.1016/j.jeconom.2014.08.002.10.1016/j.jeconom.2014.08.002Search in Google Scholar

Gençay, R. F., F. Selçuk, and B. Whitcher. 2002. An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. San Diego: Academic Press.10.1016/B978-012279670-8.50004-5Search in Google Scholar

Gençay, R., N. Gradojevic, F. Selçuk, and B. Whitcher. 2010. Asymmetry of Information Flow Between Volatilities Across Time Scales.” Quantitative Finance 10 (8): 895–915. doi:10.1080/14697680903460143.10.1080/14697680903460143Search in Google Scholar

Gerlach, H. M. S. 1988. “World Business Cycles under Fixed and Flexible Exchange Rates.” Journal of Money, Credit, and Banking 20: 621–632. doi:10.2307/1992288.10.2307/1992288Search in Google Scholar

Gomez, D. M., G. J. Ortega, and B. Torgler. 2012. “Synchronization and Diversity in Business Cycles: A Network Approach Applied to the European Union.” Working Paper 2012-01, Center for Research in Economics, Management and the Arts, Switzerland. http://www.crema-research.ch/abstracts/2012-01.htm.Search in Google Scholar

Inklaar, R., R. Jong-A-Pin, and J. de Haan. 2008. “Trade and Business Cycle Synchronization in OECD Countries – A Re-examination.” European Economic Review 52: 646–666. doi:10.1016/j.euroecorev.2007.05.003.10.1016/j.euroecorev.2007.05.003Search in Google Scholar

Jagrič, T., and R. Ovin. 2004. “Method of Analyzing Business Cycles in a Transition Economy: The Case of Slovenia.” The Developing Economies 42: 42–62. doi:10.1111/j.1746-1049.2004.tb01015.x.10.1111/j.1746-1049.2004.tb01015.xSearch in Google Scholar

Koopman, S. J., and J. V. E. Azevedo. 2003. “Measuring Synchronization and Convergence of Business Cycles for the Euro Area, UK and US.” Oxford Bulletin of Economics and Statistics 70: 23–51. doi:10.1111/j.1468-0084.2007.00489.x.10.1111/j.1468-0084.2007.00489.xSearch in Google Scholar

Kose, M. A., C. Otrok, and C. H. Whiteman. 2008. “Understanding the Evolution of World Business Cycles.” Journal of International Economics 75: 110–130. doi:10.1016/j.jinteco.2007.10.002.10.1016/j.jinteco.2007.10.002Search in Google Scholar

Lachaux, J.-P., E. Rodriguez, J. Martinerie, and F. J. Varela. 1999. “Measuring Phase Synchrony in Brain Signals.” Human Brain Mapping 8: 194–208. doi:10.1002/(SICI)1097-0193(1999)8:4<194::AID-HBM4>3.0.CO;2-C.10.1002/(SICI)1097-0193(1999)8:4<194::AID-HBM4>3.0.CO;2-CSearch in Google Scholar

Lachaux, J.-P., E. Rodriguez, M. Le Van Quyen, A. Lutz, J. Martinerie, and F. J. Varela. 2000. “Studying Single-Trials of Phase Synchronous Activity in the Brain.” International Journal of Bifurcation and Chaos 10: 2429–2439. doi:10.1142/S0218127400001560.10.1142/S0218127400001560Search in Google Scholar

Le Van Quyen, M., J. Foucher, J.-P. Lachaux, E. Rodriguez, A. Lutz, J. Martinerie, and F. J. Varela. 2001. “Comparison of Hilbert Transform and Wavelet Methods for the Analysis of Neuronal Synchrony.” Journal of Neuroscience Methods 111: 83–98. doi:10.1016/S0165-0270(01)00372-7.10.1016/S0165-0270(01)00372-7Search in Google Scholar

Lee, J. 2012. “Measuring Business Cycle Comovements in Europe: Evidence from a Dynamic Model with Time-Varying Parameters.” Economics Letters 115: 438–440. doi:10.1016/j.econlet.2011.12.125.10.1016/j.econlet.2011.12.125Search in Google Scholar

Mardia, K. V., and P. E. Jupp. 1999. Directional Statistics. Chichester: Wiley.10.1002/9780470316979Search in Google Scholar

Massmann, M., and J. Mitchell. 2004. “Reconsidering the Evidence: Are Euro Area Business Cycles Converging?” Journal of Business Cycle Measurement and Analysis 1: 275–307. doi:10.1787/jbcma-v2004-art16-en.10.1787/jbcma-v2004-art16-enSearch in Google Scholar

Percival, D. B., and A. T. Walden. 2000. Wavelet Methods for Time Series Analysis. Cambridge: Cambridge University Press.10.1017/CBO9780511841040Search in Google Scholar

Raihan, S. Md., Y. Wen, and B. Zeng. 2005. “Wavelet: A New Tool for Business Cycle Analysis.” Federal Reserve Bank of St. Louis Working Paper 2005–050A. http://research.stlouisfed.org/wp/more/2005-050.10.20955/wp.2005.050Search in Google Scholar

Ramsey, J., 2002. “Wavelets in Economics and Finance: Past and Future.” Studies in Nonlinear Dynamics and Econometrics 6 (3): 1–27. doi:10.2202/1558-3708.1090.10.2202/1558-3708.1090Search in Google Scholar

Savva, C. S., K. C. Neanidis, and D. R. Osborn. 2010. “Business Cycle Synchronization of the Euro Area with the New and Negotiating Member Countries.” International Journal of Finance and Economics 15: 288–306. doi:10.1002/ijfe.396.10.1002/ijfe.396Search in Google Scholar

Selesnick, I. W. 2002. “The Design of Approximate Hilbert Transform Pairs of Wavelet Bases.” IEEE Transactions on Signal Processing 50: 1144–1152. doi:10.1109/78.995070.10.1109/78.995070Search in Google Scholar

Selesnick, I. W., R. G. Baraniuk, and N. G. Kingsbury. 2005. “The Dual-Tree Complex Wavelet Transform. A Coherent Framework for Multiscale Signal and Image Processing.” IEEE Signal Processing Magazine 22: 123–149. doi:10.1109/MSP.2005.1550194.10.1109/MSP.2005.1550194Search in Google Scholar

Whitcher, B. J., and P. F. Craigmile. 2004. “Multivariate Spectral Analysis Using Hilbert Wavelet Pairs.” International Journal of Wavelets, Multiresolution and Information Processing 2: 567–587. doi:10.1142/S0219691304000652.10.1142/S0219691304000652Search in Google Scholar

Witte, H., P. Putsche, C. Hemmelmann, C. Schelenz, and L. Leistritz. 2008. “Analysis and Modeling of Time-Variant Amplitude-Frequency Couplings of and Between Oscillations of EEG Burst.” Biological Cybernetics 99: 139–157. doi:10.1007/s00422-008-0245-x.10.1007/s00422-008-0245-xSearch in Google Scholar PubMed

Xue, Y., R. Gençay, and S. Fagan. 2013. “Jump Detection with Wavelets for High-Frequency Financial Time Series.” Quantitative Finance 14 (8): 1427–1444. doi:10.1080/14697688.2013.830320.10.1080/14697688.2013.830320Search in Google Scholar

Yogo, M. 2008. “Measuring Business Cycle: A Wavelet Analysis of Economic Time Series.” Economics Letters 100: 208–212. doi:10.1016/j.econlet.2008.01.008.10.1016/j.econlet.2008.01.008Search in Google Scholar

Supplemental Material

The online version of this article (DOI: 10.1515/snde-2014-0081) offers supplementary material, available to authorized users.

Published Online: 2015-5-21
Published in Print: 2015-12-1

©2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Fourier inversion formulas for multiple-asset option pricing
  3. Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks
  4. Testing the relationships between shadow economy and unemployment: empirical evidence from linear and nonlinear tests
  5. Business cycle (de)synchronization in the aftermath of the global financial crisis: implications for the Euro area
  6. Amplitude and phase synchronization of European business cycles: a wavelet approach
  7. On the relationship between oil and gold before and after financial crisis: linear, nonlinear and time-varying causality testing
  8. Stock market’s reaction to money supply: a nonparametric analysis
https://doi.org/10.1515/snde-2014-0081
Keywords for this article
amplitude synchronization; business cycle; phase synchronization; wavelets

Articles in the same Issue

  1. Frontmatter
  2. Fourier inversion formulas for multiple-asset option pricing
  3. Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks
  4. Testing the relationships between shadow economy and unemployment: empirical evidence from linear and nonlinear tests
  5. Business cycle (de)synchronization in the aftermath of the global financial crisis: implications for the Euro area
  6. Amplitude and phase synchronization of European business cycles: a wavelet approach
  7. On the relationship between oil and gold before and after financial crisis: linear, nonlinear and time-varying causality testing
  8. Stock market’s reaction to money supply: a nonparametric analysis
Downloaded on 29.4.2026 from https://www.degruyterbrill.com/document/doi/10.1515/snde-2014-0081/html?lang=en
Scroll to top button