Following recent works from Lavancier et. al., we study the covariance structure of the multivariate fractional Gaussian noise. We evaluate several parameters of the model that allow to control the correlation structure at lag zero between all the components of the multivariate process. Then, we specify an algorithm that allows the exact simulation of multivariate fractional Gaussian noises and thus fractional Brownian motions. Illustrations involve the estimation of the Hurst exponents of each of the components.
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