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This paper presents a new approach to AutoRegressive Moving Average (ARMA or ARX) modeling which automatically seeks the best model order to represent investigated linear, time invariant systems using their inputloutput data. The algorithm seeks the ARMA parameterization which accounts for variability in the output of the system due to input activity and contains the fewest number of parameters required to do so. The unique characteristics of the proposed system identification algorithm are its simplicity and efficiency in handling systems with delays and multiple inputs. We present results of applying the algorithm to simulated data and experimental biological data. In addition, a technique for assessing the error associated with the impulse responses calculated from estimated ARMA parameterizations is presented. The mapping from ARMA coefficients to impulse response estimates is nonlinear, which complicates any effort to construct confidence bounds for the obtained impulse responses. Here a method for obtaining a Zineurizution of this mapping is derived, which leads to a simple procedure to approximate the confidence bounds.