A linear time-varying stochastic system described in terms of input-output data corrupted by noise is given and an optimal, time-invariant, low-order approximating model is required. After the problem statement, the paper introduces an input-independent criterion and then considers the problem of its evaluation from the available data. A procedure is developed in order to obtain in closed form the upper bound, corresponding to a given level of probability, of the error functional. Finally, the minimization of this quantity leads to the optimal model parameters and to the approximation measure.