Page - 163 - in The Austrian Business Cycle in the European Context

163 it has been shown that this type of filter does not only leave the rather erratically moving high frequencies above the business cy- cle spectrum inside but superimposes them, instead. Despite this, it has been shown that the impact of this superimposition on the de- tection of lead and lag structures between time series is only mar- ginal. Results of cross-correlations and coherence statistics are just reduced in their size (and significance) compared with the other filtering methods. Only for those series where these high-frequency components themselves possibly show some cross-correlation, overall cross-correlations shifted upward. This was the case for construction, where weather conditions interfere with the produc- tion of several sectors. Differences between HP- and BK-filtered data concerning cross- correlations and coherences were quite small. The HP filter is able to cancel out trends of deterministic or stochastic nature up to an order of four and leaves high-frequency variations above the business cycle spectrum inside, but without superimposing them. The minor difference between comovements of HP- and BK- filtered data mirrors the dominance of business cycle variations in most of our time series, so that the inclusion of high-frequency parts disturbs this picture only to a minor extent. From a theoretical point of view, the BK filter captures best the idea of the business cycle concept. The researcher can make ex- plicit what he or she defines as business cycle variations. For the present study, a frequency band retaining all cycles between two and eight years' length has been used. In order to filter out these frequencies rather sharply, we allowed six observations on either end of all time series to be sacrificed. In doing so, the problem of leakage (i.e. keeping frequencies outside the desired band wrongly inside and filtering correct ones out) has been reduced significantly.