Six different methods for the parameter estimation of linear time-invariant discrete systems are compared for the case when the output and its delayed components are obscured by autocorrelated noise. These methods are least squares, instrumental variables, orthogonal regression and the generalized forms of these methods. The comparison is done for different noise levels and for the uniform and normal error distributions. It was found that, on average, generalized least squares gave the best results and were the most robust computationally. But when the obviously faulty cases were discarded, generalized instrumental variables gave the best results. The latter was most susceptible to roundoff errors when noise to signal ratios exceed 50% and when the roots of the model approach the unstable region. It was also found that, on average, for all methods the estimate of the constant offset was the best, followed closely by the estimates of the delayed output. These were mostly reliable. The estimates of the inpu...