Page - 32 - in The Austrian Business Cycle in the European Context

32 lows for changes in the trend behaviour over time as long as the changes are not too frequentss. An advantage over the HP filter is that the BK filter cancels out higher frequencies above the cyclical variations, too, whereas the former - acting as a pure high-pass filter - still gives an erratic but de-trended output. This can be seen again in Figure 2. The BK filter cancels out lower frequencies dedicated to the trend frequencies below 1t/3. This allows the filter to be applied theoretically even to non-seasonally-adjusted series. A further advantage is that the loss of frequency information due to data aggregation seems to be less of a problem for band-pass filters than for the HP filter. Aadland (2005) has shown that aggre- gated high-pass filtered data (e.g. by the HP filter) can lead to spurious cycles at the business cycle frequencies, if the disaggre- gated data carried strong variations in the high frequency area. This is due to the so-called "aliasing"-problem which arises when high frequency data are observed at lower frequencies. As the BK filter is symmetric like the HP filter, it causes no phase shift. A convenient feature of the BK filter is its transparency. The user can explicitly fix the upper and lower level of the band to be fil- tered; thereby defining what should be understood as the business cycle. Furthermore, the degree of approximation to the ideal band-pass version can be chosen. This can be done by sacrificing observations towards either end point in order to make the filter work more exactly, i.e. to reduce its leakage. The problem of leakage arises with the approximation of the filter. As it is not pos- sible in practice to work with infinitely long time series, shorter filters have to be applied. This has two consequences: First, frequencies can pass which should be filtered out and some are mistakenly fil- tered out which should pass; and second, frequencies are super- imposed at the borders of the frequency band, which appears as 55 See Canova (1998).