There is a surge in the literature of nonparametric Bayesian inference on multivariate time series over the last decade, many approaches consider modelling the spectral density matrix using the Whittle likelihood which is an approximation of the true likelihood and commonly employed for Gaussian time series. Meier et al. (2019) proposes a nonparametric Whittle likelihood procedure along with a Bernstein polynomial prior weighted by a Hermitian positive de_nite (Hpd) Gamma process. However, it is known that nonparametric techniques are less effcient and powerful than parametric techniques when the latter specify the parameters which model the observations perfectly. Therefore, Kirch et al. (2019) suggests a nonparametric correction to the parametric likelihood in the univaraite case that takes the effciency of parametric models and amends sensitivities through the nonparamtric correction. Along with this novel likelihood, the Bernstein polynomial prior equipped with a Dirichlet process wight is employed. My current work is to extend the corrected Whittle likelihood procedure to the multivariate case, this will be done by combining the work of Meier et al. (2019) and Kirch et al. (2019). Precisely, the multivariate version of the corrected Whittle likelihood is proposed along with the Hpd Gamma process weighted Bernstein polynomial prior to implement Bayesian inference. A key study of this work is to prove the posterior consistency. In the talk, I will review the work done by Meier et al. (2019) and Kirch et al. (2019), then an introduction of the multivariate corrected Whittle likelihood procedure will be given.