  This paper deals with the identification of the multivariate fractional
Brownian motion, a recently developed extension of the fractional Brownian
motion to the multivariate case. This process is a $p$-multivariate
self-similar Gaussian process parameterized by $p$ different Hurst exponents
$H_i$, $p$ scaling coefficients $\sigma_i$ (of each component) and also by
$p(p-1)$ coefficients $\rho_{ij},\eta_{ij}$ (for $i,j=1,...,p$ with $j>i$)
allowing two components to be more or less strongly correlated and allowing the
process to be time reversible or not. We investigate the use of discrete
filtering techniques to estimate jointly or separately the different parameters
and prove the efficiency of the methodology with a simulation study and the
derivation of asymptotic results.
