G. Ferrari-Trecate and G. De Nicolao. NARX models: Optimal parametric approximation of nonparametric estimators. Technical Report AUT00-25, Automatic Control Laboratory, ETH Zurich, 2000. http://control.ethz.ch/
Bayesian regression, a nonparametric identification technique with several appealingfeatures, can be applied to the identification of NARX (nonlinear ARX) models. However, itscomputational complexity scales as $O(N^3)$ where $N$ is the data set size. In order toreduce complexity, the challenge is to obtain fixed-order parametric models capable ofapproximating accurately the nonparametric Bayes estimate avoiding itsexplicit computation. In this work we derive, optimal finite-dimensional approximations ofcomplexity $O(N^2)$ focusing on their use in the parametric identification of NARX models.