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short recession then this will strengthen the growth tendencies
via the integral term mentioned above.
What is to be avoided is an image of the cycle in which there is
fluctuation round a pre-determined trend; I am myself guilty of
having used the, simile of a ”badly functioning controller” which
after a time always returns to a given long term path. There is a
negative feedback (characteristic of the controller) but the long
term path to which it pushes the system is itself influenced and
shaped by the course of the trade cycle!
Now on the face of it it would seem th"at a linear equation, since
its independent solutions are combined by superposition to give
the resulting time series, could not represent the interdependence
of trend and cycle. In actual fact,however, the solution depends
on initial conditions,and, the process being frequently
interrupted by exogenous disturbances,the initial conditions
change (changing phase,amplitude and trend ). An ex post
statistical analysis of^ the time series will not easily reveal the
trend and the cycle wj^lch constitute the theoretical solution of
the equation, even yi we do not allow for possible changes in the
parameters in the^course of time.
We turn now to the question what the "long term memory” can mean
in the concrete. There are in principle two possibi1ities:It can
involve a positive feedback,and then it will tend to perpetuate an
existing trend; or it can involve a negative feedback,and then it
will lead to a long wave and not a trend.
J