Page - 93 - in The Austrian Business Cycle in the European Context

93 Table 2: Differences in cross-correlations' BK minus HP HP minus fod BK minus fod aufF --0.01 --0.06 --0.07 autCDE 0.06 0.21 0.27 autGDP 0.01 0.09 0.10 autGHI 0.01 0.13 0.14 autGVA 0.01 0.03 0.04 autJK --0.03 --0.05 --0.08 eurGDP 0.06 0.26 0.32 eurGDPex 0.08 0.21 0.29 gerCDE 0.03 0.26 0.29 gerF 0.09 0. 17 0.26 gerGDP 0.07 0.35 0.42 gerGHI 0.07 0.30 0.37 gerGVA 0.07 0.34 0.41 gerGVAex 0.07 0.33 0.40 gerJK 0.01 0.28 0.29 Sum 0.60 2.85 3.45 Source: Own calculations. - 1 For abbreviations used see the list of abbreviations on page B. 8.2. 1.2 Coherence A statistic closely related to the cross-correlation is the coherence, given in the next column of Tables A la to c 106• Instead of showing the linear comovement in the time series domain, it is defined in the frequency domain using cross-spectra, as explained in chap- ter 5, equation (23). The table shows the proportion of spectral mass within the frequency band between 6 and 32 quarters after smoothing the frequencies by a Bartlett spectral window of three quarters' length. This gives triangular weights w (n) for the frequen- cies which are calculated according to 106 As the cross-spectrum is also defined over complex values, only the modulus of the squared cross-spectra is taken instead. The root of the resulting squared coher- ence is used here.