This paper proposes a methodology to enhance the estimation of parameter matrices in multivariate autoregressive models. It uses the Kalman filter and state space representation to improve the precision of parameter estimation, while achieving low computational burden. Two methods of covariance matrix adaptation are considered within the Kalman filter framework, namely, the forgetting factor and simulated annealing. Although both methods improve the estimator convergence rate while preserving precision, the former is preferred. The methodology is tested on simulated data as well as on electroencephalographic recordings. As a result, a reduction up to 40% of computational burden is achieved, but reconstruction error reaches as much as 3%.