Pitfalls of the parametric approaches exploiting cross-validation for model order selection*

Prediction error methods (PEM) are often used to identify a dynamic system starting from input-output samples. In particular, in the classical parametric scenario models of different order are identified from data and compared using the cross validation (CV) paradigm where measurements are split into a training and a validation data set. However, some inefficiencies related to this popular approach to system identification have been recently pointed out. This paper provides some insights on the reasons of such pitfalls, clarifying why PEM equipped with CV may lead to estimators with large variance and a poor predictive capability on new data.