In this paper an identification problem is solved which is directed towards the use of the identified model as a basis for robust control design. A procedure is presented to identify, on the basis of time domain measurement data, a reduced order finite impulse response (FIR) model together with an upper bound on the model error of the corresponding transfer function, using only minor prior information. We assume the measurement data to contaminated with a stochastic noise disturbance unknown spectral properties. By applying a procedure similar to Bartlett’s procedure of periodogram averaging, in conjunction with a periodic input signal, the statistics of the model error asymptotically can be obtained from the data. The model error consists of two parts : a probabilistic part, due to the stochastic noise disturbance, and a worst-case part, due to the unmodelled dynamics. The latter is explicitly bounded with a hard error bound, while for the former a confidence interval can be specified asymptotically. This enables an explicit trade-off between undermodelling (bias) and variance terms. The resulting error bound appears to be tight.