We propose a decomposition of financial time series into Gaussian subsequences characterized by a constant H¨older exponent. In (multi)fractal models this condition is equivalent to the subsequences themselves being stationarity. For the different subsequences, we study the scaling of the variance and the bias that is generated when the Hoelder exponent is re-estimated using traditional estimators. The results achieved by both analyses are shown to be strongly consistent with the assumption that the price process can be modeled by the multifractional Brownian motion, a nonstationary process whose H¨older regularity changes from point to point.