To identify parametric models for stochastic systems, the standard least-squares method tends to yield biased parameter estimates owing to correlated residuals resulting from unknown stochastic disturbances. Although the consistency properties of parameter estimates could generically be secured by instrumental variable methods, the inadequate choices of instruments and prefilters would render them Much less efficient. This article establishes a method to identify an ARARX (AutoRegressive AutoRegressive with eXogenous input), an ARMAX (AutoRegressive Moving Average with eXogenous input), or a BJ (Box-Jenkins) model based on the process output data smoothed by the EWMA (Exponentially Weighted Moving Average). The major advantages of the method are 2-fold. First, the proposed off-line and online algorithms often acquire unbiased, efficient, and consistent parameter estimation from identification tests operating in open loop or closed loop. Second, the resultant process plus disturbance model can be easily employed to remove the autocorrelation in process data for accurate statistical process monitoring. Monte-Carlo simulation Studies demonstrate that the proposed method provides reliable parametric models for a wide variety of noise characteristics and is highly robust with respect to the sampling period, sample size, and noise-to-signal ratio.