Business cycle synchronization according to wavelets – the case of Poland and the euro zone member countries

In the paper time-frequency analysis in the form of the maximal overlap discrete wavelet transform (MODWT) and its complex variant – the maximal overlap discrete Hilbert wavelet transform (MODHWT) is applied to study changing patterns of business cycle synchronization between Poland and 8 euro zone member countries (France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal and Spain). We also touch upon the endogeneity hypothesis of the optimum currency area criteria and ask about the recent changes in business cycle variability and their influence on the level of synchronization. Wavelet analysis is a very convenient way of studying business cycles as it possesses good localization properties and is highly efficient in extracting time- -varying frequency content of time series. In the paper we make use of these properties and provide a detailed characterization of the degree of business cycle synchronization among the countries under study as well as of the changing amplitudes of business cycles which are measured here as the appropriate frequency components of industrial production indices. In the examination we apply wavelet analysis of variance, wavelet correlation and cross-correlation examination as well as wavelet coherence and wavelet phase angle analysis in their global and (or) local (short-term) versions. The empirical examination points at an increasing synchronization of the Polish business cycle with the euro zone cycles as well as a fairly stable level of business cycle synchronization among the euro zone countries themselves.