Application of cross-spectral analysis to research in dynamics of economic processes in Germany

Wiesław Łuczyński


Spectral analysis serves recognition of harmonic structure of time series.  Cross-spectral analysis is in fact a joint and simultaneous spectral analysis of two time series.  Establishing connections and relations between two time series appearing in different frequencies is the aim of cross-spectral analysis.

The phase spectrum (phase shift) of the industrial production, the employment and the forecast of the economic activity of the industrial production of Germany demonstrate the linear and positive relation for low frequencies (in which we observe considerable values for the squared coherency).  It would suggest that the changes of long waves in the employment and in forecasts of the economic activity of industrial production remain ahead of the appropriate changes in the dynamics of industrial production of Germany.  We observe a similar relationship in case of the phase DAX spectrum and unemployment. However, in case of the phase DAX spectrum and prices of industrial goods the linear relationship is negative, which suggests lag changes in prices of industrial goods in relation to changes of a DAX share index.

For considerable values of the squared coherency we observe a negative linear relation of the phase spectrum of two time series which suggests lag phases of manufacture of cement in relation to economic activity indicators in the construction in the area of low frequencies. 

The carried out cross-spectral research shows that in the analyzed period the dynamics of industrial production of Germany and the dynamics of DAX share index are correlated with the dynamics of chosen economic processes in different frequencies of trade cycle.  It is possible then to talk about symptoms of correlated cyclical behaviors.  Revealing the diversified phase spectrums and gains in low as well as in high frequencies of cyclical fluctuations, the examined time series in German economy deserves special attention.  Therefore, cross-spectral analysis can be an effective tool supporting the process of constructing barometers of economic activity, the policy of stabilization or economic recovery.


spectrum; cross-spectrum; squared coherency; cross-amplitude; phase spectrum

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