Page - 66 - in The Austrian Business Cycle in the European Context

66 tions for the identification of peaks and troughs. There is no possi- bility to take into account the amplitude of cyclical variations and, as it is a purely deterministic approach, nor the uncertainty en- countered when choosing dates for the turning points. As this procedure proposed by Bry - Boschan (l 971) was devel- oped originally only for monthly data, some amendments have been proposed to use it analogically for quarterly series90• The ver- sion used in this study is the one implemented in the BUSY software package developed by the Joint Research Centre of the Euro- pean Commission (1993). There, de-trended time series are smoothed by a Spencer curve, which is a symmetric 2:x7 moving average filter with the following weights 1 [74+67(L+L-1)+46(L2 +L-2)+2l(L3 +L-3)+ ] (30J v(L)= 320 3(L4 +L-4)-5(L5 +L-5)-6(L6 +L-6)-3(L7 +L-7) In order to compensate the loss of seven data points on either end of the series, the series is extended by extrapolating the growth of the first and last four observations. This smoothed series is used, first of all, for replacing outliers in the uncorrected series, which are de- tected by imposing that its standard deviation be a certain multi- ple of the series total standard deviation, to be defined by the user. Following this, the series corrected for outliers is filtered by a 2 x 4 term MA term in the quarterly time series case. The output of this filter and the one generated by the Spencer curve are both scanned for common turning points, which are characterised by local minima or maxima with intervals of five periods91 • Further- more, a minimum phase length of 6 quarters is imposed, together with an alternation of the signs of the turning points. 90 Harding -Pagan (2002) is an example in this respect. 91 The size of the interval can be altered by the user.