Application of Modified Information Criterion to Multiple Change Point Problems

The modified information criterion (MIC) is applied to detect multiple change points in a sequence of independent random variables. We find that the method is consistent in selecting the correct model, and the resulting test statistic has a simple limiting distribution. We show that the estimators for locations of change points achieve the best convergence rate, and their limiting distribution can be expressed as a function of a random walk. A simulation is conducted to demonstrate the usefulness of this method by comparing the powers between the modified information criterion and the Schwarz information criterion. 1991 AMS Subject Classification: Primary 62H15; Secondary 62H10.