Adaptive model selection for polynomial NARX models

Two algorithms are proposed for the adaptive model selection of polynomial non-linear autoregressive with exogenous variable (NARX) models. The recursive forward regression with pruning (RFRP) algorithm is based on a recursive orthogonal least-squares (ROLS) procedure and efficiently integrates model augmentation and pruning to reduce processing time whenever new data are available. The algorithm provides excellent model structure tracking compared to different OLS-based model selection policies. A less accurate but much faster algorithm that can be used for time-critical applications is the ROLS-LASSO. This algorithm uses a recursive version of the least absolute shrinkage and selection operator (LASSO) regularisation approach for structure selection. It features a recursive standardisation of the regressors and performs parameter estimation with ROLS. A sliding window data updating is here adopted for both algorithms, although the methods seamlessly generalise to exponential windowing with forgetting factor. Some simulation examples are provided to demonstrate the model tracking capabilities of the algorithms.