  Operator fractional Brownian motion (OFBM) is the natural vector-valued
extension of the univariate fractional Brownian motion. Instead of a scalar
parameter, the law of an OFBM scales according to a Hurst matrix that affects
every component of the process. In this paper, we develop the wavelet analysis
of OFBM, as well as a new estimator for the Hurst matrix of bivariate OFBM. For
OFBM, the univariate-inspired approach of analyzing the entry-wise behavior of
the wavelet spectrum as a function of the (wavelet) scales is fraught with
difficulties stemming from mixtures of power laws. The proposed approach
consists of considering the evolution along scales of the eigenstructure of the
wavelet spectrum. This is shown to yield consistent and asymptotically normal
estimators of the Hurst eigenvalues, and also of the coordinate system itself
under assumptions. A simulation study is included to demonstrate the good
performance of the estimators under finite sample sizes.
