  We study the asymptotic behavior as $n\to \infty$ of the sequence
$$S_{n}=\sum_{i=0}^{n-1} K(n^{\alpha} B^{H_{1}}_{i})
(B^{H_{2}}_{i+1}-B^{H_{2}}_{i})$$ 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.
