A Wavelet Approach to Synchronization of Output Cycles

The dynamic comovement between time series is a key concept in macroeconomic analysis. The extent to which series are cyclically synchronized is particularly important for evaluating the feasibility of common policy measures for groups of countries. This paper investigates concepts in the time domain and in the frequency domain that have traditionally been used to detect and describe such cyclical comovements in output data. However, methods from the former category cannot account for different cycle lengths, while the statistics from the latter category fail to capture transient relationships. Therefore, the use of multivariate wavelet analysis and a modification of the cohesion statistic from Fourier analysis is suggested to simultaneously assess comovement at the frequency level and over time for both country pairs and larger aggregates. The main finding from applying this method to output cycles is that synchronization does indeed vary across both dimensions and that important events during the time span of the sample, such as the introduction of the Euro, can be visualized. As a further benefit of the wavelet approach, it turns out to be hardly sensitive to the technique employed to extract the cyclical component from the output series.