  Self-similarity is widely considered the reference framework for modeling the
scaling properties of real-world data. However, most theoretical studies and
their practical use have remained univariate. Operator Fractional Brownian
Motion (OfBm) was recently proposed as a multivariate model for
self-similarity. Yet it has remained seldom used in applications because of
serious issues that appear in the joint estimation of its numerous parameters.
While the univariate fractional Brownian motion requires the estimation of two
parameters only, its mere bivariate extension already involves 7 parameters
which are very different in nature. The present contribution proposes a method
for the full identification of bivariate OfBm (i.e., the joint estimation of
all parameters) through an original formulation as a non-linear wavelet
regression coupled with a custom-made Branch & Bound numerical scheme. The
estimation performance (consistency and asymptotic normality) is mathematically
established and numerically assessed by means of Monte Carlo experiments. The
impact of the parameters defining OfBm on the estimation performance as well as
the associated computational costs are also thoroughly investigated.
