Information criterion of seriously over-fitting change-point models

摘要

It is shown that a general class of information criteria is able to rule out seriously over-fitting change-point models where the number of change points is comparable to the sample size. Equivalently speaking, it is not necessary to impose a pre-specified upper bound on the number of change points when we search for the optimal solution as in Bardet, Kengne, and Wintenberger (2012). For the time series with finite but unknown number of change points, the model with consistently estimated number of change points tends to be preferred to any other models (even seriously over-fitting) under such a class of information criteria. The results hold under a broad class of time series model introduced in Bardet and Wintenberger (2009) that includes ARMA-GARCH as a special case. Since exhaustive search of all possible change-point models for the optimal information criterion value is computationally infeasible, it is common to impose certain restrictions on the searching range. The applications of the information criterion to the restricted search of the optimal model are also discussed.