1 Abstract This paper presents and discusses the simulation of time stochastic ARMA systems and the development of an oo line identiication based on a prediction error method combined with exponential forgetting. The simulation involves diierent stages, starting with the simulation of the Gaussian white noise as an input to the original system and, the simulation with a combined signal and Gaussian white noise (ARMAX model). Simulation of time variation is also based on Gaussian white noise for a higher complex error variation. Stability tests on the time system are achieved and appropriate measures are taken to improve the feasibility and stability of the system. This paper is intended to present the simulation of mathematical models based on completely observed input-output dynamical systems. In the analysis and design of control systems, it is of high importance to have a mathematical model of a given system that describes the system dynamics as completely and accurately as possible. System descriptions can be achieved through para-metric models which are accepted as mathematical models. Limiting the work to Linear Time Varying (LTV) system description, the question can be bounded to the identiication of the parameters of a dynam-ical input-output observed system. The identii-cation can be achieved through the estimation of those parameters. A general technique in handling time systems is to simulate the system with Gaus-sian white noise and to assume the system is in a similar environment. Even though this assumption complicates the estimation process, it provides an excellent opportunity to test the Auto Regression and the Gauss-Newton minimization algorithms for high complex dynamical outputs. System identiication tool box is derived by L. Ljung, 2]. The tool box was designed for Linear Time Invariant (LTI) which does not satisfy the time variation as an initial requirement. Furthermore , the tool box ARMAX provides equal weights, which also contradict the need for exponential forgetting where recent data are given more weight. For this paper, most of those functions were rewritten to satisfy the initial requirements. This simulation works only for multiple-input-single-output problems.