Page - 99 - in The Austrian Business Cycle in the European Context

99 Not only the proportion of the total variation of the data set ex- plained by the common factors, but also the proportion reflected in each time series is of interest. Table A 7 gives for all three filtering methods the proportion of variation explained by the two com- mon factors reflected by the respective time series. In the case of first-order-differenced data (the FOO section of Table A 6), both common factors are able to explain more than 70 percent of the variance of the series autGV Aex, gerCDE and gerGVAex, which is quite in line with theory. However, the variation of euro area GDP excluding Austria and Germany is only explained to one-half (48 percent) by both factors. In all cases (except in the case of the Austrian financial intermediation, real estate and business service sector), the explanatory power of the common component in- creases by moving from the first-order-difference data to HP- and BK-filtered ones, supporting the view that idiosyncratic cycles are primarily a high-frequency phenomenon. This result can also be obtained by looking at the average over all series given in the bot- tom line or by forming averages over all frequencies up to the second eigen value of Tab/es A 5 a to c. In the BK-filtered data case, the common factors are capable of explaining nearly 70 percent of the variation of the euro area GDP series ( again ex- cluding Austria and Germany). Furthermore, the value for the Aus- trian industrial production has improved considerably to nearly 80 percent. The explanatory power of the two common factors is especially strong for those series responding typically to business cycle movements. This supports the view that the variance repre- sented by the two common factors is close to something that can be considered as the business cycle. Furthermore, the exception- ally low values for some series like the construction industry in Aus- tria and Germany and financial intermediation, real estate and business activities are quite in line with theory which suggests that these sectors have a low connection to the business cycle. As the variation of the common factors represented in each of the series can be regarded as cleaning them by their idiosyncratic variations, the difference between looking at frequency-filtered series alone and series transformed by our dynamic factor model