NARX model selection based on simulation error minimisation and LASSO

The simulation error minimisation (SEM) approach is very effective for polynomial non-linear autoregressive with exogenous variables (NARX) model selection, but is typically limited to the exploration of candidate regressor sets of limited size because of the computational cost involved in model simulation and the complexity of the empirical structure selection process over large candidate regressor sets. This study investigates the combination of a SEM algorithm for model selection, known as simulation error minimisation with pruning (SEMP), with the least absolute shrinkage and selection operator, which operates a regularisation that balances model accuracy with size in parameter estimation. The combined approach can greatly reduce the computational effort of the SEMP, without significantly affecting its accuracy, and sometimes improve the model selection quality with respect to the plain SEMP.