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, $$2p_0$$ 2 p 0 , in regular models. In change-point models, it is not twice the number of parameters, $$2m+2p_m$$ 2 m + 2 p m , because of their irregularity, where $$m$$ m and $$p_m$$ p m are the numbers of the change-points and the other parameters, respectively. In this study, the asymptotic bias is shown to become $$6m+2p_m$$ 6 m + 2 p m , which is simple enough to conduct an easy change-point model selection. Moreover, the validity of the AIC is demonstrated using simulation studies. Copyright The Institute of Statistical Mathematics, Tokyo 2015