Autoregressive moving average systems with exogenous inputs (ARMAX) are widely used in a variety of applied problems connected with identification, adaptive control and time series analysis. This paper proposes the method which enables one to estimate parameters in the ARMAX system with a prescribed mean-square precision at the termination time. The procedure is constructed on the basis of sequential analysis approach and makes use of special modifications of estimates obtained by the method of instrumental variables. The method can be used for guaranteed estimation (in mean-square sense) of spectral density of ARMA processes. Copyright 2002 IFAC