Page - 74 - in The Austrian Business Cycle in the European Context

74 7.3 The intrinsic lead and lag classification of dynamic factor models In 4.2.1, the index model approach has been presented, with spe- cial focus on the dynamic factor model as proposed by Forni et al. (2000). This approach tries to capture the dynamics of the whole set of observed time series, by extracting several common com- ponents. These components are identified not only by looking at simultaneous comovements, but also by their leading and lagging properties. Such a common component is shown with different in- tensity in the different time series, as can be observed by the fac- tor loadings necessary to explain the variance of a special series. In order to make use of the intrinsic lead and lag classification of the dynamic components model, the phase angle shifts of all se- ries compared with (or in relation to) a reference series have to be calculated99. This is equivalent to the calculation of mean leads and lags in the frequency domain statistic as presented in 7. 1 . 7.4 Concordance indicator A further indicator that offers some insight into the comovement of two series has been proposed by Harding - Pagan (2002). They constructed a statistic - called "concordance indicator" - which measures the fraction of time where both series are simultaneously in the same state. (40) Ij, = n-1 [# ~jt = 1,S,, = 1}] + n-1 ~ ~jl = o,s,, = o}] = n-1 {I sj, s,, + {1-s1,)(1-s,,)} 99 This reference series can be the common component included in GDP, GVA or industrial production.