Predictor estimation via Gaussian regression

A novel nonparametric paradigm to model identification has been recently proposed where, in place of postulating finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite-dimensional space. In this paper, we extend such nonparametric approach to the design of optimal predictors by interpreting the predictor coefficients as realizations of Gaussian processes. Numerical experiments, where data are generated by ARMAX models, are used to show advantages of the new approach in terms of both predictive capability on new data and accuracy in reconstruction of predictor coefficients. In a companion paper, it is also shown how this new approach to predictor design may greatly enhance performance of subspace identification methods.