Change-point model selection via AIC

Change-point problems have been studied for a long time not only because they are needed in various fields but also because change-point models contain an irregularity that requires an alternative to conventional asymptotic theory. The purpose of this study is to derive the AIC for such change-point models. The penalty term of the AIC is twice the asymptotic bias of the maximum log-likelihood, whereas it is twice the number of parameters, $$2p_0$$2p0, in regular models. In change-point models, it is not twice the number of parameters, $$2m+2p_m$$2m+2pm, because of their irregularity, where $$m$$m and $$p_m$$pm are the numbers of the change-points and the other parameters, respectively. In this study, the asymptotic bias is shown to become $$6m+2p_m$$6m+2pm, which is simple enough to conduct an easy change-point model selection. Moreover, the validity of the AIC is demonstrated using simulation studies.