Stock Returns Declustering Under Time Dependent Hölder Exponent

Two of the most important stylized facts well-known in finance relate to the non-Gaussian distribution and to the volatility clustering of stock returns. In this paper, we show that a new class of stochastic processes – called Multifractional Processes with Random Exponent (MPRE) – can capture in a very parsimonious way both these “anomalies”. Furthermore, we provide evidence that the sole knowledge of functional parameter characterizing the MPRE allows to calculate residuals that perform much better than those obtained by other discrete models such as the GARCH family.