Page - 35 - in The Austrian Business Cycle in the European Context

35 Empirical studies of economic time series for the Netherlands car- ried out by Kranendonk - Bonenkamp - Verbruggen (2004) have shown a better performance with regard to revisions of the end- point output than with the BK filter. Nevertheless, the use of asym- metrical type filters suffers from phase shifts or they contain an im- plicit forecast (based on past observations), respectively. Whether a thorough forecast combined with the BK filter yields a better per- formance depends on the specific case. In the literature, modifications of this approach can be found, like in Altissimo et al. (2001) who applied a multivariate Christiano- Fitzgerald filter in order to study business cycles for the euro area. Goldrian - Lehne ( 1999) proposed a further band-pass filter that is not based on a minimisation process, but on the common pattern of weight matrices, instead. 3.2.4.7 The Beveridge-Nelson decomposition Instead of filtering time series for special frequency bands, Beveridge - Nelson ( 1981) proposed a time series model-based approach. The idea behind is that after fitting a time series model to the underlying data, its structure can be explored in order to separate the trend from the cycle. The fitting of an ARIMA model58 implicitly models the trend as a stochastic process59• The stationary ARMA part is assumed to be (or at least contains) the business cy- cle. In order to show some interesting properties of this approach, a simple example is set up. Assuming the underlying time series can be modelled by an ARIMA (0, 1, 1) process, the time series be- comes stationary after forming first order differences. This can be 58 In the case of not-seasonally adjusted data, a S-ARIMA model has to be applied. 59 In most cases it will be of order one, which implicitly yields a random walk proc- ess.