Page - 36 - in The Austrian Business Cycle in the European Context

36 represented by a moving average process of order 1 and shows at the same time the cycle: {11) fl y1 = e1 + /3 e, _ 1 where fly, is the (log) differenced time series, e, a white noise term and p represents the moving average parameter with /J < 1 . If this expression is solved recursively and the start values are as- sumed Yo = e0 = o , the following expression emerges t t-1 (12) y,=Le;+/JLe; i=l i=l or I {13) y,=(l+fJ)Le;-/Je, i=l In (13) the first term y, = (1 + /J )I e; is the trend part which - being a random walk process - is the sum of its past shocks, and p e, repre- sents our stationary cyclical part. Equation (13) implies one inter- esting feature of this kind of splitting the trend from the cycle: The secular as well as the cyclical component are both driven by the same shock at the particular point in time. This means, trend and cycle are perfectly correlated60• In order to make this somewhat clearer, we can transform (13) to showing that the trend as well as the cyclical component at time t both depend on shock e. This implication is in stark contrast to the 60 See Canova (1998). p. 481.