—The article deals with a class of stochastic
processes, the Multifractional Processes with Random
Exponent (MPRE), recently introduced to gain flexibility in
modeling many complex phenomena. We claim that MPRE can
capture in a very parsimonious way most of the well known
financial stylized facts. In particular, we prove that the process
unconditional distributions are fat-tailed and high-peaked and
show that, as it occurs for asset returns, the empirical
autocorrelation functions of the process increments are close to
zero whereas significant values are exhibited by squared (or
absolute) increments. Furthermore, we provide evidence that
the sole knowledge of functional parameter of the MPRE allows
to calculate residuals that perform much better than those
obtained by other discrete models such as the GARCH family.
—Declustering, GARCH, Multifractional
Processes with Random Exponents, Residuals.
Sergio Bianchi is with University of Cassino, Via S. Angelo, 03043
Cassino (Italy) (phone: +39-0776-299-4846; fax: +39-0776-299-4834;
Alexandre Pantanella is with University of Cassino, Via S. Angelo, 03043
Cassino (Italy) (phone: +39-07762994845; fax: +39-07762994834; e-mail:
Cite:Sergio Bianchi and Alexandre Pantanella, "Pointwise Regularity Exponents and Well-Behaved Residuals in Stock Markets," International Journal of Trade, Economics and Finance vol.2, no.1, pp. 52-60, 2011.