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.
