Seite - 79 - in The Austrian Business Cycle in the European Context

79 8. Results In this chapter, several methods of the tool box presented above are applied to various data sets, which are processed with differ- ent filtering methods. This combination of methods, data and treatments will give some insight into the robustness of results for dating the Austrian business cycle. Apart from the extensive work- load, a comparison of results across all theoretically possible com- binations between data sets and methods would be more confus- ing than enlightening. Therefore, we confine ourselves to the most common or most appropriate combinations, from a theoretical point of view. 8.1 Isolation of business cycle frequencies As already mentioned in chapter 3, there exist several methods for isolating possible business cycle characteristics from time series. Some of them are indirect in that they try to wipe out all other in- formation that should not be contained in the business cycle component, and others try to isolate the business cycle directly. It was decided to employ three methods for the present study: 8. 1. 1 First-order differences This method was mainly selected for its popularity. Here, first-order differences to the preceding quarter of logged data were con- structed, which give approximately growth rates, as it was pointed out in chapter 6.1. Such growth rates are very often used as a rule- of-thumb for dating the business cycle and they are called growth rate cycles. Using this method for de-trending implicitly assumes that the trend is of stochastic nature and integrated of order 1 . As pointed out in the theoretical part, a violation of this ( 1) assumption can shift the true business cycle out of the observed frequency window. It the