Page - 43 - in The Austrian Business Cycle in the European Context

43 same purpose, but in this case the method comes close to uni- variate methods like the ones presented in chapter 4.2. Using this reference chronology, several statistics can be calcu- lated in order to classify the series as leading, lagging or coinci- dent. The most popular statistics in the time domain are cross- correlations and means, medians and standard deviations of leads and lags. In the frequency domain the calculation of co- herences is used frequently. Other possible measures - along with their properties - are discussed in chapter 5. As a result, all time se- ries have to be classified into separate sets of leading, lagging and coincident economic time series. In order to construct one composite index for each class, a spe- cific weight (ranging from O to 100) is given to each according to seven properties6s: • economic significance • statistical adequacy (the capability of the series to repre- sent the economic variables) • timing at recessions an expansions • conformity with historical business cycles • smoothness • timeliness (timely availability of the data) • stability with regard to revisions Subsequently, a restriction allowing only the best-performing series (according to these criteria) to enter the composite indices has to be implemented. Again, there are different methods of aggrega- tion in order to obtain only one indicator from several time series. Basically, standardisation methods accounting for the different variabilities of the time series, detrending steps (usually clearing for 65 See Zarnowitz -Boschan (1975).