Statistical analysis of financial time series is studied. We use wavelet analysis to study signal to noise ratios along with auto-correlation function to study correlation length for time series data of daily stock prices for specific sectors of the market. We study the "high beta" stocks versus the "low beta" stocks. We sample ten companies from both of these sectors. We find that the signal to noise ratio is not uniformly high for the "high beta" classified stocks nor is the correlation length large for the "high beta" classified stocks. We explain reasons for this and possible further applications.