Asymptotic theory for fractional regression models via Malliavin calculus

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire SAmos-Marin Mersenne 2 LPP - Laboratoire Paul Painlevé

Abstract : oindent We study the asymptotic behavior as $n\to \infty$ of the sequence $$S {n}=\sum {i=0}^{n-1} Kn^{\alpha} B^{H {1}} {i} \left B^{H {2}} {i+1}-B^{H {2}} {i} ight$$ where $B^{H {1}}$ and $B^{H {2}}$ are two independent fractional Brownian motions, $K$ is a kernel function and the bandwidth parameter $\alpha$ satisfies certain hypotheses in terms of $H {1}$ and $H {2}$. Its limiting distribution is a mixed normal law involving the local time of the fractional Brownian motion $B^{H {1}}$. We use the techniques of the Malliavin calculus with respect to the fractional Brownian motion.

Author: Solesne Bourguin - Ciprian Tudor -

Source: https://hal.archives-ouvertes.fr/