A general criterion to determine the number of change-points

A general criterion is proposed to determine the number KK of the change-points in a parametric nonlinear multi-response model. Schwarz criterion is a particular case. The change-points depend on regressor values and not on instant of measure. We prove that the proposed estimator for KK is consistent. Simulation results, using Monte Carlo technique, for nonlinear models which have numerous applications, support the relevance of the theory.