Demixing operator fractional Brownian motion

In this paper, we consider the problem of demixing a multivariate stochastic process made up of independent, fractional Brownian motion entries. The observable, mixed signal is then an operator fractional Brownian motion (OFBM). The law of OFBM scales according to a Hurst matrix that affects every component of the process, which makes its estimation by univariate-like methods quite difficult. We combine a classical joint diagonalization procedure and the wavelet analysis of OFBM to produce a consistent and asymptotically Gaussian estimator of the mixing matrix. Monte Carlo experiments in dimension 4 show that the finite sample estimation performance for both the demixing and Hurst matrices is very satisfactory. We also provide limits in distribution for the eigenvalues and eigenvectors of random wavelet variance matrices as the sample size goes to infinity.