This study investigates a unified framework of the market mechanism, called the MultiFractal Market Hypothesis, that goes beyond the simple dichotomy of either extreme efficiency or extreme inefficiency by modeling financial markets as piecewise Fractional Brownian Motion (fbm) processes. Additionally, this study introduces the application of Wavelet Transforms, a recently developed technique from the field of signal processing, to the area of financial economics. The multifractal model is tested by using wavelet transforms to estimate the Hurst exponent (H) of fbm's for different subintervals of monthly and daily data for various equity and bond markets in the U.S. domestic area, and weekly data for equity markets in the international area. The results indicate the presence of antipersistet (H < 1/2), random walk (H = 1/2), and persistent (H > 1/2) subperiods, and thus, indicate that the multifractal market hypothesis warrants further consideration. These results have implications for modern financial theory suggesting that there is scope for more general multifractal asset pricing and portfolio selection models to be developed.