Page - 105 - in The Austrian Business Cycle in the European Context

105 Apart from requiring consecutive turning points to show alternat- ing signs (so that a trough has to be followed by a peak), the minimum cycle length (the time between two peaks or troughs) has been set at 6 quarters and the one for the minimum phase length (the time between two consecutive turning points of differ- ent signs) to 3 quarters. If there are two potential turning points of the same sign, only the lowest (in the case of troughs) or highest (in the case of peaks) is retained. A further problem arises as turning points following each other have to possess different signs. Therefore, identifying the first one can be very important for estimating all following ones. As the Spencer curve smoothes the series very strongly, the first turning point was identified after applying a 2 x 4 term moving average at the beginning of the series. Figures A 1 a to d show the resulting dates of the turning points for various series and different methods of cycle extraction as graphs. It can be observed that the number of turning points detected110 varies considerably across the methods for business cycle extrac- tion. The first-order-difference-filtered series shows the lowest num- ber of turning points, namely 10, and their occurrence is concen- trated at the beginning of the series. In the HP-filtered case, 11 turning points have been identified which are spread more or less equally over the time span. The series with the BK-filtered data shows the largest number of turning points. 15 of them have been discovered, and again they are spread more or less equally over the entire time series. This picture seems to be stable for all different time series within the respective approach. Figure A 1 b shows the turning points of euro area GDP excluding Germany and Austria, and Figure A 1 c those of German gross value added excluding agriculture and forestry. 110 A triangle pointing upwards marks a trough with its top pointing to the lowest point of the trough. Accordingly, triangles pointing downwards marl< peaks.