Page - 75 - in The Austrian Business Cycle in the European Context

75 where Ij, is the concordance indicator between time seriesj and the reference series r, both of length n, and si, and s" being 1 if they are in expansion or 0 if in contraction. It is defined over the interval [ 1, 0] where 1 indicates total pro-cyclicality and 0 perfect counter-cyclicality. If both are exactly pro-cyclical this concor- dance indicator is 1 and 0 if they are perfectly counter-cyclical. This indicator allows no classification of leading and lagging prop- erties of turning points but just of their simultaneous behaviour, if the time series are not shifted in time. 7.5 Standard deviation of the cycle There are also statistics which concentrate on the size of up- and downturns, as this can be important for economic policy purposes. The simplest statistic in this area is probably the standard deviation of the business cycle component. This measure is constructed as (41) O'= n with ji, being the mean of the observed series, n the number of observations and Yr1 the observation itself. Vijselaar - Albers (2001) used this kind of method to show the ex- posure of several countries to the euro area cycle. They reported for three different periods the standard deviations of HP-filtered time-series for manufacturing production and GDP. This can be regarded as a simple but crude measure, as it is not clear whether these variations stem from a common or an idiosyncratic cycle, or even from a variation erroneously passing the filter.