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Some aspects of the discrete wavelet analysis of bivariate spectra for business cycle synchronisation


  • Bruzda, Joanna


The paper considers some of the issues emerging from the discrete wavelet analysis of popular bivariate spectral quantities such as the coherence and phase spectra and the frequency-dependent time delay. The approach utilised here is based on the maximal overlap discrete Hilbert wavelet transform (MODHWT). Firstly, via a broad set of simulation experiments, we examine the small and large sample properties of two wavelet estimators of the scale-dependent time delay. The estimators are the wavelet cross-correlator and the wavelet phase angle-based estimator. Our results provide some practical guidelines for the empirical examination of short- and medium-term lead-lag relations for octave frequency bands. Further, we point out a deficiency in the implementation of the MODHWT and suggest using a modified implementation scheme, which was proposed earlier in the context of the dual-tree complex wavelet transform. In addition, we show how MODHWT-based wavelet quantities can serve to approximate the Fourier bivariate spectra and discuss issues connected with building confidence intervals for them. The discrete wavelet analysis of coherence and phase angle is illustrated with a scale-dependent examination of business cycle synchronisation between 11 euro zone countries. The study is supplemented by a wavelet analysis of the variance and covariance of the euro zone business cycles. The empirical examination underlines the good localisation properties and high computational efficiency of the wavelet transformations applied and provides new arguments in favour of the endogeneity hypothesis of the optimum currency area criteria as well as the wavelet evidence on dating the Great Moderation in the euro zone.

Suggested Citation

  • Bruzda, Joanna, 2011. "Some aspects of the discrete wavelet analysis of bivariate spectra for business cycle synchronisation," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 5, pages 1-46.
  • Handle: RePEc:zbw:ifweej:201116

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    References listed on IDEAS

    1. H. Wong & Wai-Cheung Ip & Zhongjie Xie & Xueli Lui, 2003. "Modelling and forecasting by wavelets, and the application to exchange rates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(5), pages 537-553.
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    Cited by:

    1. Bruzda Joanna, 2015. "Amplitude and phase synchronization of European business cycles: a wavelet approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 625-655, December.

    More about this item


    Hilbert wavelet pair; MODHWT; wavelet coherence; wavelet phase angle; business cycle synchronisation; euro zone;

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies
    • O52 - Economic Development, Innovation, Technological Change, and Growth - - Economywide Country Studies - - - Europe


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