Page - 55 - in The Austrian Business Cycle in the European Context

55 5. Analysing cyclical comovements After extracting the business cycle, an analysis about the leading and lagging properties of several economic time series is of great interest80• There exists a broad range of statistics in this respect, which can be classified according to their belonging to time or frequency domain statistics. It is worth mentioning that this kind of analysis already forms an implicit part of the dynamic common component approach and constitutes an essential part of the identification and extraction of the business cycle. 5.1 Time domain statistics for analysing comovements To this class all sort of statistics belong, which exhibit comovements between time series at discrete points in time or for certain inter- vals. They are mainly based on correlation statistics referring to second moments of time series. Calculating cross-correlations in order to detect potential leads and lags is the simplest form of identifying comovements between the business cycle and other series. They are constructed as (22) Cov(zb.i• zs.,-,) Pb.s (t') = -;:::===== Jvar(zb.,) Var(zs.,) with the subscript b denoting the business-cycle-carrying time se- ries (i.e. the reference series). s = 1, ... , N counts for all other N time series and -r determines the different leads and lags for which cross-correlations are calculated. If -r = O the synchronised co- movement is observed. The classification as leading or lagging is mainly based on the delay with which the highest cross-correlation is achieved. It can only be regarded as clear-cut, if the cross- eo As the dating procedure of the business cycle is so prominent, this will be han- dled separately in the next chapter together with some analysis on turning points.