Developing a new BIC for detecting change-points

Usual derivation of BIC for the marginal likelihood of a model or hypothesis via Laplace approximation does not hold for a change-point which is a discrete parameter. We provide an analogue l BIC, which is a lower bound to the marginal likelihood of a model with change points and has an approximation error up to O_p(1) like standard Schwartz BIC. Several applications are provided covering simulated r.v.'s and real financial figures on short-term interest rate.