A novel approach to analyzing time series generated by complex systems. suc
h as: markets, is presented. The basic idea of the approach is the Law of S
elf-Similar Evolution, according to which any complex system develops self-
similarly. There always exist some internal laws governing tile evolution o
f 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 h
idden internal laws defining the system character. This problem can be solv
ed by employing the self-similar approximation theory which supplies the ma
thematical foundation for the law of self-similar evolution. In this report
, the theoretical basis of the new approach to analyzing time series is for
mulated, with an accurate explanation of its principal points.