Seite - 33 - in The Austrian Business Cycle in the European Context

33 side-lobes. As Woitek (2001) pointed out, this could possibly lead to spurious results in business cycle analysis. But the leakage problem as well as the one of amplified side-lobes can both be reduced by using longer-term filters and sacrificing more observations at either end of the time series. Applying the BK filter, one has the possibility to individually select the trade-off between the accuracy of the filter and the end-point problem. Compared with this, the HP filter properties depicted in the gain function of Figure 2 are calculated by accepting a loss of two observations at either end of the time series. It can be seen, that the precision of the filtering process at rr/ 16 is not as exact as in the BK filter case. Furthermore, the part in the middle of the business cycle frequency band is superimposed (values above l) and there is some leakage at higher frequencies. Figure 3 shows how the precision of the filtering process changes if one is willing to sacrifice a higher number of observations at the start and the end of the series. Figure 3a shows the gain function obtained by a BK filter with a window length of 6 quarters, causing a loss of 3 quarters at either end. Compared with this, the 12- quarter-window filter (resulting in a loss of 6 quarters at both ends like it is used in our calculations) cuts out more precisely the de- sired frequencies, without strongly superimposing business cycle frequencies and with a lower leakage. But this precision is ob- tained at the cost of losing the possibility of analysing the business cycle at the margin. As this is the period for which the dating is most important in order to take timely economic policy measures, this can be regarded as a drawback. To overcome this problem, some authors propose an extension of the time series by applying forecasting techniques. Fiorentini - Planas (2003) propose an ARIMA forecast for that purpose. But all forecasts based on univariate time series methods (without includ- ing external information like business survey data) may reduce the