Input-output parametric models for non-linear systems Part II: stochastic non-linear systems

In the first part of this paper (Leontaritis and Billings 1984) recursive input-output models for deterministic non-linear multivariate discrete-time systems were derived and sufficient conditions for their existence were defined. In this the second part, the non-linear model is compared with other system representations, several examples are introduced and the results are extended to create prediction error input-output models for multivariable non-linear stochastic systems. These latter models are a generalization of the ARMAX models for linear systems and are referred to as NARMAX or non-linear autoregressive moving average models with exogenous inputs.