  We make use of wavelet transform to study the multi-scale, self similar
behavior and deviations thereof, in the stock prices of large companies,
belonging to different economic sectors. The stock market returns exhibit
multi-fractal characteristics, with some of the companies showing deviations at
small and large scales. The fact that, the wavelets belonging to the
Daubechies' (Db) basis enables one to isolate local polynomial trends of
different degrees, plays the key role in isolating fluctuations at different
scales. One of the primary motivations of this work is to study the emergence
of the $k^{-3}$ behavior \cite{hes5} of the fluctuations starting with high
frequency fluctuations. We make use of Db4 and Db6 basis sets to respectively
isolate local linear and quadratic trends at different scales in order to study
the statistical characteristics of these financial time series. The
fluctuations reveal fat tail non-Gaussian behavior, unstable periodic
modulations, at finer scales, from which the characteristic $k^{-3}$ power law
behavior emerges at sufficiently large scales. We further identify stable
periodic behavior through the continuous Morlet wavelet.
