302 Investigating Economic Trends and Cycles
of 5. Elsewhere, it has been given a high value of 100,000, which results in trend
segments that are virtually linear.
6.11 Summary and conclusions
When confronted by the wide variety of methods that are available for extracting
the components of an econometric data sequence, a practitioner is liable to ask for
a recommendation of the best method. In the case of business cycle analysis, there
can be no unequivocal answer. The choice of an appropriate method will depend
both on the nature of the data and on the purpose of the analysis. It may also
depend on the aesthetic preferences of the analyst.
Nevertheless, the choice of a method ought to be made with a view to its effects
in the frequency domain. Econometricians working with temporal sequences are,
nowadays, paying increasing attention to the frequency aspects of their analyses,
and this is where the major emphasis of the present chapter has been placed.
One of the difficulties in analyzing business cycles is that there is no unequiv-
ocal definition of what constitutes a trend. Often, a clearly defined structure that
combines the trend and the cycles can be discerned within the data. An example
of the successful extraction of a combination of trend and cycles that has been
identified by spectral methods is provided by Figure 6.15. However, there is hardly
ever a case where the data indicates a point within the frequency spectrum of this
structure where the trend ends and the cycles begin.
The only unequivocal definition of the trend that might be offered is that it must
have a monotonic trajectory that is devoid of cycles, which means, in practice, that
it should be modeled by a polynomial of low degree. This was the practice of the
generation of pioneering econometricians to which Tintner belonged.
Latterly, this approach has fallen out of favour amongst econometricians. Now-
adays, they are liable to describe polynomial trends as deterministic trends, which
are contrasted with stochastic trends. The latter are regarded as capable of more
realistic representations of economic behavior. In particular, a stochastic trend
can represent a cumulation of random events that effect the development of an
economy in the course of time, in the way that the circumstances of their early
lives can affect the physical statures of human beings.
Polynomial trends are an essential element within linear models of stochastic
accumulation, whether they be represented in continuous time or in discrete time.
Therefore, although the conceptual distinction may be a clear one, the practical
distinction between a stochastic trend generated by an ARIMA process and a poly-
nomial trend buried in noise is by no means as clear cut as, at first, it might seem
to be.
The distinction becomes even more tenuous in the case of an ARIMA model
that incorporates stochastic drift. Therefore, notwithstanding the recent efforts of
several econometricians, it does not seem to us to be fruitful to employ statistical
tests in an attempt to determine which of these alternative statistical structures
actually underlies the data.