Seite - 98 - in The Austrian Business Cycle in the European Context

98 gerGV Aex: German gross value added excluding agriculture and forestry ger JK: German services in financial intermediation, real estate and business activities It has to be stressed again that this is a rather small set of time se- ries as index models have been developed to reduce the cross- section dimension of time series while keeping their main variation characteristics. A justification for using such a small set has been given in chapter 4. 1 .2. and the results presented in the following will show that this method can work quite successfully despite this small data set. Using the method outlined in chapter 4.1 .2., two common factors have been extracted from the data set. These two factors to- gether describe more than 60 percent of the total variation of the data set, which can be seen in Tables A 5 a to c. Additional fac- tors would explain an even larger proportion, but would also raise the danger of reflecting idiosyncratic cycles. Tables A 5 a to c show the proportions of variation explained at different frequen- cies of the data set for the first 7 eigen values. In the case at hand, the spectral density matrix is evaluated for 7 frequencies over the interval (0,1t) 109• It turns out that the two factors used describe very well the total variation of the data set for all three filtering methods and over all given frequencies. In the first-order-difference case, the proportion of variance explained by the first two factors (rep- resented here by their eigen values) exceeds 50 percent and goes up to 60 percent with BK-filtered data. An additional third com- mon factor would explain only around 1 0 percent more of the to- tal variance, which seems too little for considering it as a business cycle variation. 109 This high number of frequencies has been chosen in order to facilitate a proper classification of the time series as leading or lagging.