MULTIFRACTIONAL PROPERTIES OF STOCK INDICES DECOMPOSED BY FILTERING THEIR POINTWISE HÖLDER REGULARITY

Abstract

We propose a decomposition of financial time series into Gaussian subsequences characterized by a constant Hölder 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 Hölder 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 Hölder regularity changes from point to point.