Goodness of fit assessment for a fractal model of stock markets

An assessment of the goodness of fit of a new stochastic model of stock dynamics is investigated. The model is the multifractional Brownian motion (mBm), introduced independently by Péltier and Lévy Véhel (1995) [2] and Benassi (1997) [3]. The analysis concerns the (un)conditional distributions of log-variations of the Dow Jones Industrial Average (DJIA). By comparing the performance of mBm with respect to a Garch (1,1), we argue that the former captures the distributional features as well as the pathwise empirical ones displayed by the U.S. Dow Jones index, while the Garch (1,1) works better in global terms.