Page - 92 - in The Austrian Business Cycle in the European Context

92 The sum over all differences in cross-correlations, given in the last row, shows that the overall difference between the BK and the HP method is rather small, whereas it is substantial compared with the first-order-difference case, especially with the BK method. This find- ing contrasts with the results for the leading and lagging properties found similar between the first-order differences and the HP method. The superimposition of higher-frequency movements, as it results from the first-order-difference procedure, seems to reduce cross-correlations dramatically. Only for autF (the Austrian con- struction sector) and autJK (financial intermediation services and real estate, renting and business activities), the cross-correlations calculated on the basis of first-order-difference-filtered data are higher than those of the other methods. It is quite plausible that for the construction sector the methods that include (or superimpose) higher frequency variations (like weather conditions) show a stronger cross-correlation with the reference series (which also in- cludes these variations) than others. But it has to be borne in mind, that this comovement is not one of a business cycle nature and therefore beyond our scope of interest. As a result, looking only at the highest cross-correlations for differ- ent lags, the methods including higher-frequency variations (like the HP filter or the first-order differences) give very similar results. BK-filtered data show a slightly different pattern, but the output shows highest cross-correlations that are not farer away than ± 1 quarter compared with the other two methods. Focusing on the size of the highest cross-correlations, largest values can be found in the BK-filter case, followed by the HP-filter output, and the one based on first-order differences are smallest. Only for those sectors where systematic high-frequency variances (like weather or dis- crete events) could play a role, the methods including this infor- mation should show higher cross-correlations.