The development and maintenance of accurate predictive models for dynamic systems are highly challenged by system complexity, limited information (i.e., data), changing cross and time correlation structures and changing model parameters. Thus, for a model or modeling method to achieve long term success in implementation into a real system, it must be phenomenologically sound and adaptive, as well as being capable of immediate update from recently obtained process data (i.e., plant data). A model is phenomenologically sound when its structure accurately captures physical input and output relationships, and the stochastic behavior of process and measurement noise. On-line adaptive methods are critical to success because process variations that cause changes to noise correlation structures and model coefficients are frequent in real systems. A common occurrence in non-adaptive, off-line, model identification is the requirement of a new model by the time the model is ready for implementation due to significant process variations. For a method to have on-line adaptive abilities, it must be capable of using process data (which have a low signal to noise ratio, and limited range over the operating space) to update its fitting performance.