Page - 19 - in The Austrian Business Cycle in the European Context

19 the series. In a graphical representation of a time series they are marking a one-time spike in the plot32• Level shifts are innovations which mark a break in the time series, shifting the successive mean by a constant value. They appear as an upward or downward step in the time series. Transitory components are outliers lasting only for a limited time and vanishing thereafter. They are either fading out in successive time periods (decay) or they evolve slowly over time and vanish suddenly (ramp). Some of these outliers can be explained by variables outside this model. Ignored working day variables or weather conditions - in- fluencing the economic output - are examples. Furthermore, every unusual strong movement in the history of a time series may appear as an outlier. In this special case here, this goes for sharp recessions, too. It is a difficult task to detect outliers and one has to define first of all what should be considered an outlier and by which value it has to be replaced. For the present study, outlier detection has been carried out by modelling all time series as seasonal ARIMA models with regression effects (sometimes also called Reg-SARIMA models for short), which took care of the varying number of working days of differ- ent countries by regressing on them. Several steps of estimation are carried out in order to check whether an elimination of the significant outliers (in this study dummy variables with a t-value higher then 3.8) improves the following model33• A purely me- 32 It has to be borne in mind that in a first-order differenced time series an additive outlier marks a spike with a counter-reaction in the next period. If no counter- reaction follows, it appears as a level shift in the original series. 33 This procedure was assisted by the software package TRAMO developed by Gomez - Marava/1 ( 19921. It is widely used also in business cycle studies like for ex- ample in Artis -Krolzig -Toro (2004), Artis -Marcellino -Proietti (2004) and Altissimo eta/. (2001}.