A randomized algorithm for nonlinear model structure selection

The identification of polynomial Nonlinear Autoregressive [Moving Average] models with eXogenous variables (NAR[MA]X) is typically carried out with incremental model building techniques that progressively select the terms to include in the model. The Model Structure Selection (MSS) turns out to be the hardest task of the identification process due to the difficulty of correctly evaluating the importance of a generic term. As a result, classical MSS methods sometimes yield unsatisfactory models, that are unreliable over long-range prediction horizons. The MSS problem is here recast into a probabilistic framework based on which a randomized algorithm for MSS is derived, denoted RaMSS. The method introduces a tentative probability distribution over models and progressively updates it by extracting useful information on the importance of each term from sampled model structures. The proposed method is validated over models with different characteristics by means of Monte Carlo simulations, which show its advantages over classical and competitor probabilistic MSS methods in terms of both reliability and computational efficiency.