Page - 25 - in The Austrian Business Cycle in the European Context

25 this method is applied to a series for which the logarithm has been taken, the outcome can be interpreted as growth rates. Therefore the basic assumptions behind the method of applying first-order differences are that the trend component of the series corresponds to a random walk process without drift, that the cy- clical component is stationary and that the two components are uncorrelated42• The original time series y, is assumed to have a unit root, which is entirely due to the trend component of the series43• This assumption of a random walk trend gives anything but a smooth profile of the trend component, which is for example the case in the Solow growth model. Every shock to this trend will never decay in impact in the future. Nevertheless, this assumption is still popular in empirical economics since the pioneering work of Nelson - Plosser ( 1982) who found unit roots in 13 out of 14 long- term annual US macro series, including real GDP44• In the case of a time series model based on seasonally adjusted data, this behaviour can be represented as (2) y1 =x1 +c1 +&1 y, is our trended aggregate, c, the cycle to be extracted and e, some white noise process where e, ~ N(O,cre). The assumption of a random walk trend implies that x, = y, _ 1 which, entered into (2), gives 42 See Canova ( 1998). 43 There are also multivariate forms of this approach. Cheung - Westermann ( 1999) estimated the trend of industrial net production as the co-integration relation be- tween Germany and Austria. Business cycle effects are captured by the residual short- run relationship not included in the error correction term. 44 Since then, several authors (e.g. Rudebusch, 1993 and Diebold -Senhadji, 1996) have challenged these findings by showing that the testing procedure has not enough power against economically relevant trend-stationary alternatives.