EXTENDING SELF-SIMILARITY FOR FRACTIONAL BROWNIAN-MOTION

The fractional Brownian motion (fBm) model has proven to be valuable in modeling many natural processes because of its persistence for large time lags. However, the model is characterized by one single parameter that cannot distinguish between short- and long-term correlation effects. This work investigates the idea of extending self-similarity to create a correlation model that generalizes discrete fBm referred to as asymptotic fBm (afBm). Namely, afBm is parameterized by variables controlling short- and long-term correlation effects. We propose a fast parameter estimation algorithm for afBm based on the Haar transform, and we demonstrate the performance of this parameter estimation algorithm with numerical simulations.