Page - 67 - in The Austrian Business Cycle in the European Context

67 An additional, less smoothed, series is calculated by further short- ening to MA order according to a parameter called QCD (quar- ters of cyclical dominance). This QCD yields the minimum delay for which the average of absolute deviations of growth in the Spencer cycle is larger than that in the irregular component. This series is again checked for common turning points with the series as calculated before, subject to the same requirements for cycle length and the alternation of signs. As this last short filter is able to move close to the end of the series - while for the longer filters syn- thetic extrapolations had to be made - turning points found in the last or first two observations are dropped. Versions of the Bry-Boschan routine used for dating the quarterly US-GDP time series have been quite successful in tracking the turn- ing points as published by the NBER92• 6.3 Hidden Markovian-switching processes Studies resorting to the method proposed by Hamilton ( 1989) try to represent the business cycle component by a Markov-switching autoregressive model. Here, the series examined is to be repre- sented by a stochastic process that can switch between a con- tractive and an expansionary regime93• In its most general form, not only the mean µ is allowed to vary between both states, but also the AR parameters efJ of order p and the variance of the error term (with assumed zero mean) e, . (31} z, = µ,1 + f ;,, z,_; +e:1 i=I 92 Examples for this kind of studies ore King - Plosser (1994) and Harding - Pagan (2003). 93 In Artis - Krolzig - Toro (2004) a third regime is considered for some countries, in order to capture the effect of a break in trend growth in the second half of the seventies.