Page - 96 - in The Austrian Business Cycle in the European Context

96 their coincident comovements, the different statistics informing about leads and lags of the various time series do not. While the mean delay would justify classifying autJK as lagging by one pe- riod, the cross-correlation was highest for coincident data. GerGHI, for its part, would be classified as lagging by one quarter accord- ing to the frequency-domain-based method, whereas rmax is high- est at a three-quarters lag in the time domain108• The largest differ- ence between both approaches in the first-order-difference case can be observed for the German financial, real estate, renting and business services (gerJK). Whereas the mean delay indicates a lead by one-fourth of a quarter (0.21), the cross-correlation sta- tistics suggest a lag by one year ( ,max at minus four quarters). For the HP-filtered data case, differences are not that large be- tween the information about leads and lags given by cross- correlations and mean delays. None of the latter exceeds one or minus one quarter, and this is closely in line with the information provided by cross-correlations. Only in the case of gerGHI and ger JK, cross-correlations again suggests a lag of 3 or 4 quarters re- spectively, compared with the reference series, whereas mean delay statistics indicate only a small lag of approximately half a quarter. The picture is similar for BK-filtered data. The signs of the period shift seem to be the same between the cross-correlation criteria and the mean delay. Every time cross-correlation suggests a lag, this is not contradicted by the mean. But the number of periods of leads and lags indicated by cross-correlations are again much higher than according to mean delays. The criterion of cross-correlation seems less than reliable. As in the HP-and BK-filtering cases ,max for ger JK is at a lag of four quarters, but the cross-correlation at 10 is only marginally different from that. 108 Admittedly, the difference between the rm,. of 0.18 and r0 of 0.06 is quite small.