Page - 27 - in The Austrian Business Cycle in the European Context

27 correspond to over-differencing which biases the cyclicality to the high frequency spectrum, whereas in the second case under- differencing shifts it to the low frequency area45• Due to these deficiencies, the first-order difference filter has lost most of his popularity in empirical studies on business cycles. If it is used at all, it is mostly to check for robustness of the output across several methods or to illustrate its deficiencies. Despite these un- desired properties which limit the use of this filter for business cycle analysis, it will be considered in this study due to the popularity of growth-rate-based interpretations as a rule-of-thumb method46• 3.2.4.4 Hodrick-Prescott filter The use of the business cycle filter proposed by Hodrick - Prescott ( 1980) is very popular among business cycle researchers. It is a flexible tool that is capable of removing non-stationary compo- nents that are integrated of order four or less47• Effectively, the trend implicitly fitted by the HP filter amounts to a process of curve fitting. It results from constructing a trend as smooth as possible, with penalizing all squared deviations from this trend from the original time series. The precise formula is (5) T min ~)(y,-g,)2+J[(g,+1-g,)-(g,-g,_1)J2] J~O (g,Jf_ l/= 1 where y, is the original trended time series and g, is the trend to be estimated and subtracted. J is acting as the signal-to-noise ra- tion, being the weight for penalizing all deviations from trend, which has to be fixed by the user. If J = 0, there is no difference between the trend and the original series, if J approaches infinity ' 5 See e.g. Ritschl -Uebele (2006). ' 6 Like it is done by the CEPR Business Cycle Dating Committee. ' 7 See Baxter -King (1995).