Page - 95 - in The Austrian Business Cycle in the European Context

95 tote, renting and business activities (NACE J+K). This result is quite similar to the one in the time series domain. This is not surprising, as the coherence is based on a Fourier transformation of the cross- correlation function and therefore its frequency domain equiva- lent. Once again we find that total euro area GDP shows a stronger comovement with the Austrian business cycle than the series cor- rected for Germany and Austria. All three filtering methods are capturing this bias effect. The German series most closely con- nected to the Austrian reference series are gross value added with and without agriculture and the manufacturing sector (gerCDE). This result, which is quite in line with theory is robust across all methods and is mirrored in the time domain cross-correlation re- sults. Interestingly, all three methods show that the comovement between the Austrian reference series and Germany's highest- scoring series is not higher than between Austria and the euro area aggregate (corrected for Austria and Germany). This pro- vides strong evidence for the existence of a European business cycle, which would be of great importance for a common eco- nomic policy. 8.2.1.3 The mean delay In order to examine the leading or lagging properties of several time series in the frequency domain, the mean delay - as defined in 5.2.2. - has been calculated and the results are given in Ta- b/es A 1 a to c. In Table A 1 a, the first-order-difference case, none of the time series seem to lead or lag the reference series by more than one quarter. Only autJK - the Austrian sector covering finan- cial services and real estate, renting and business activities - and gerGHI - the German trade, restaurant, transport and communi- cation sector - seem to have a lag close to one quarter (-0.78 or -0.7 4, respectively). Whereas cross-correlations and their frequency domain equiva- lent, the coherences, show a rather similar picture concerning