Cross-Spectral Analysis of Long-Term Economic Cycles

One of the problems of studying economic cycles, namely long-term ones, is the choice of an adequate method that allows identifying and explaining the nature of the economic cycle according to available statistical data, which subsequently becomes the basis for predicting future economic dynamics. In addition, questions remain open not only concerning the establishment of the duration of Kondratieff cycles, but also the very fact of their existence. For this purpose, the study investigated time series of annual GDP per capita growth rates for such countries as England, France, and the Netherlands for 1820-2015. In this paper, the cross-spectral analysis approach was developed as a modelling tool for identifying long waves, the use of which, in contrast to classical Fourier spectral analysis, allows investigating the periodicity of two interrelated time series simultaneously in the frequency and time domains. As a result of the analysis, coherence and phase shift graphs were constructed for the investigated time series, which became the basis for identifying and determining the duration of economic cycles of different periods. According to the obtained results, it was found that all selected time series have a high coherence value (within the range of 0.8-0.9) in the frequency domain corresponding to K-waves with the period of 38-55 years (in the frequency range 0.025-0.015). At the same time, a slight phase shift was obtained for the frequency range corresponding to long cycles, which is an empirical confirmation of the synchronisation of the investigated time series. These facts are an additional argument for empirical confirmation of the existence of long waves. The practical significance of this study is that the identification of multi-period cycles using the proposed approach allows developing and implementing adequate counter-cyclical measures to timely regulate economic development at both the macro- and meso-levels