For a system of stochastic linear differnce equations   where the random disturbances U is a timely non-independent GAUssian process we derive BAYESian estimators for A, B and the unknown parameters the convariance function of U_t and conditions for the consistance this estimators. Further we derive BAYEsian predictors of X(T + 1) by the observation of   and the recursive form the BAYEsian estimators for time independent random disturbances U_t. For the derivation of the BAYEsian estimators and predictors conjugate prior distributions are used.