__On the Long Economical Cycles__

*Y. B. Karasik, *

Thoughts Guiding Systems Corp.,

Ottawa, Canada.

e-mail:karasik@sympatico.ca

When in the July 2003 editorial
the editor conjectured that there might be long economical cycles
spanning decades
he did not know that similar conjectures were already put forward not once in the past
(for example, by Nikolay Kondratiev in 1925).
But what surprised the editor was that there is still a controversy about existence of such cycles. To him it was pretty obvious from the theory of Fourier integral.

Any function can be represented by Fourier integral, which is basically a sum of cycles with periods ranging from 0 to infinity.
Thus, any economical variable has components with cycles of several years
as well as several decades, several centuries, several thousand years, etc.
The question is how big the variations of these components are.
If they are bigger than or comparable to the variations of components with smaller cycles then it makes sense to speak about the long economical cycles.
Otherwise they are just not easily observable components.

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Thus, the hypothesis of the long economical cycles has to be reformulated as follows: the spectrum of Fourier transform of any economical variable has several maxima, one in the proximity of several years to the origin (zero) and others much farther.
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As soon as the hypothesis of long economical cycles is specified as above from the standpoint of Fourier integral, it becomes easily provable.
Indeed, everybody knows that Dark Ages were a watershed between two such maxima, one in antiquity, and the other one in the modern times.
Thus a couple thousand years cycle definitely exists according to the available data.
It does not prove, however, the existence of Kondratiev waves of any prominence, but nevertheless confirms the existence of some long waves in affirmative.