Jackknife and bootstrap methods in the identification of dynamic models

A new criterion based on a Jackknife or a Bootstrap statistic is proposed for identifying non-parsimonious dynamic models (FIR, ARX). It is applicable for selecting the number of components in latent variable regression methods or the constraining parameter in regularized least squares regression methods. These meta parameters are used to overcome ill-conditioning caused by model over-parameterization, when fitted using prediction error or least squares methods. In all cases studied, using PLS for parameter estimation, the proposed criterion led to the selection of better models, in the mean square error sense, than when selected via cross-validation. The methodology also provides approximate confidence intervals for the model parameters and the step and impulse response of the system.