Seite - 73 - in The Austrian Business Cycle in the European Context

73 Table 1: Contingency table for turning point analysis Serles Expansion Contraction SUBTOTAL Expansion n1,1 n1,o n1,_. Contraction no.1 no.o no ... Subtotal n_.,1 n_.,o N Source: own illustration. where n1, 1 (no.o) counts the number of periods when both series are in expansion ( contraction} over the whole time span, and n1,o and n0•1 how often they are in different phase. By calculating from this some kind of statistic like the Pearson's contingency coefficient one can measure the extent of synchronised comovement of the series. This Pearson contingency coefficient is defined by (38) with (39) Pearson= J %2 z2+n Li Li (11 .. -£ .. )2 n. n . z2 = '·1 '· 1 and E . . = ,... ..., E ~, N i=O j=O i,j The same statistic can be used to determine a leading or lagging property, if one of the time series is shifted by a certain period.