  A novel approach to analyzing time series generated by complex systems, such
as markets, is presented. The basic idea of the approach is the {\it Law of
Self-Similar Evolution}, according to which any complex system develops
self-similarly. There always exist some internal laws governing the evolution
of a system, say of a market, so that each of such systems possesses its own
character regulating its behaviour. The problem is how to discover these hidden
internal laws defining the system character. This problem can be solved by
employing the {\it Self-Similar Approximation Theory}, which supplies the
mathematical foundation for the Law of Self-Similar Evolution. In this report,
the theoretical basis of the new approach to analyzing time series is
formulated, with an accurate explanation of its principal points.
