Title: Selection and estimation of fractional and multifractional models
Authors: Matthieu Garcin - Leonard de Vinci Pole Universitaire (France) [presenting]
Abstract: The Hurst exponent describes the scaling properties of a time series. One also often links its value to the persistence of the series and consequently to one's ability to forecast it: if $H=1/2$ there is no autocorrelation, if $H>1/2$ the series is persistent, and if $H<1/2$ the series is anti-persistent. However, the interpretation of the Hurst exponent strongly depends on the model describing the dynamic. We are interested in three classes of models: the fractional Brownian motion (fBm), multifractional Brownian motions (mBm), and transforms of a fBm. The mBms are extensions of the fBm and rely on the assumption that the Hurst exponent is time-varying or even is a random process, whereas it is a constant for the fBm. Transforms of the fBm, such as the fractional Ornstein-Uhlenbeck process or the Lamperti transform of a fBm, are of practical interest, for example in the fixed income world, to model stationary processes. We expose the specificities of the estimation of the Hurst exponent for all these models as well as the way one can forecast such series, using accuracy metrics that are relevant in the perspective of a portfolio manager. We also address the issue of selecting the proper fractional or multifractional model, based on the data.