Semi-automatic Non-linear Model selection

We consider model selection for non-linear dynamic equations with more candidate variables than observations, based on a general class of non-linear-in-the-variables functions, addressing possible location shifts by impulse-indicator saturation.  After an automatic search delivers a simplified congruent terminal model, an encompassing test can be implemented against an investigator's preferred non-linear function.  When that is non-linear in the parameters, such as a threshold model, the overall approach can only be semi-automatic.  The method is applied to re-analyze an empirical model of real wages in the UK over 1860-2004, updated and extended to 2005-2011 for forecast evaluation.