No. 1002

Title:

AIC for change-point models and its application

Author(s):

Ninomiya, Yoshiyuki (Kyushu University)

Key words:

Akaike's information criterion; Brownian motion; change-point model; contiguity; functional central limit theorem; random walk

Abstract:

    The purpose of this paper is to derive the Akaike's information criterion (AIC; Akaike, 1973) for general change-point models. The penalty term of the AIC is an asymptotic bias of the maximum log-likelihood multiplied by $2$, and it becomes $2p_0$ in regular models, where $p_0$ is the number of parameters. In change-point models, it is shown that the penalty term becomes $6m+2p_m$ (not $2m+2p_m$) under some contiguity condition, where $m$ and $p_m$ are the numbers of the change-points and the other parameters, respectively.