Information Theoretic Approach to Mutiple Change-Points Analysis

Abstract

The testing and estimation of multiple covariance change points for a sequence of -dimensional (m>1) Gaussian random vectors by using Schwarz information criterion (SIC) have been studied. We will estimate the number of change points as well as their locations. The consistency of the estimator is proved. The unbiased SIC is also obtained. Then asymptotic null distribution of the test statistic is derived. The result is applied to the weekly prices of Exxon and General Dynamics stocks (m=2) from 1990 to 1991, and changes are successfully detected. Key words and phrases: change-points; information criterion; SIC; unbiased SIC; asymptotic distribution; consistency; percentage points.