Page - 46 - in The Austrian Business Cycle in the European Context

46 A drawback of this static approach is that one of the basic f ea- tures of the business cycle, its auto-regressive development, is not considered since it is assumed that the factors are identically and independently distributed. In order to overcome this drawback, Stock - Watson ( 1989, 1991) proposed a method whereby a single coincident common factor is allowed to move auto-regressively of order 2 and the idiosyncratic ones are represented by AR(]) proc- esses. Again as in ( 15) ( 16) Z;,, = A; F, + U;,, i = l, ... ,p but now a special auto-regressive structure is demanded for the factors and for the components specific to each time series (18) u;,, =pu;_,_1 +u;,, with &, and u;., assumed to be white noise terms mutually inde- pendent in order to allow a proper identification of the common factors. This is usually done by writing all equations above in state space form (with ( 16) representing the measurement equation and ( 17) and (18) the respective transition equations) and gener- ating maximum-likelihood estimators by the Kalman filter. This approach is capable of extracting a common dynamic factor - showing business cycle AR properties - from the whole set of ob- served time series. It is also possible to capture more than one common factor, but in this case the identification of the first com- mon factor influences the following. Thus the number of consid- ered common factors is crucial for the output. A further possible drawback of this approach is "that it cannot be directly extended to analyse large data sets due to computational problems", as Gayer - Genet (2006) pointed out.