Page - 24 - in The Austrian Business Cycle in the European Context

24 series. The residual is taken to represent the business cycle (and the remaining components). Instead of a linear trend, other poly- nomial functions of time are possible. With the study of Nelson - Plosser ( 1982), this approach has lost most of its popularity. For the U.S., they found that a large part of economic time series are al- legedly difference stationary, where the trend cannot be re- moved by linear de-trending. For this reason, this method is not state-of-the-art and should not be considered as an option further on in the present study. 3.2.4.2 Phase-average trend This is a heuristic method of determining the trend of non-station- ary time series, usually applied in the classical business cycle framework for estimating the amplitudes of business cycle varia- tions of trended time series. Basically, it consists of the following steps40: After identifying the turning points in the trended time se- ries, it is split up into segments between two consecutive turning points (called "phases"). For each of these segments the mean is calculated (this is the "phase-average"). In order to obtain the trend for the whole series, these averages are combined with a smoothing three-term moving average. As this method of trend extraction requires an ex-ante determination of the turning points, it is not suitable for this study41 • 3.2.4.3 First-order differencing Here, de-trending is made by deducting the value at time t - 1 from t in order to get stationary differences {if they are first-order difference stationary which is in most cases assumed or tested). If "° A detailed description of the full procedure can be found in Boschan - Ebanks (1978). 41 Breuss ( 1984) has used this approach for isolating the Austrian business cycle.